Australia:
Most titles: the great Karrie Webb who won 7 between 1999-2006. Webb has a career Grand Slam (Nabisco Championship in 2000 and 2006, LPGA Championship in 2001, US Open in 2000 and 2001, du Maurier Classic in 1999, and British Open in 2002). Her signature moment of dominance came in the 2000 Nabisco Championship where she won by a whopping 10 strokes. This was followed up by an 8-stroke victory at the 2001 US Open. She rounded out her career by beating up-and-coming Lorena Ochoa in a playoff in 2006.
Runner-up: Jan Stephenson was one of the few non-American golfers prior to the 90s to have multiple golf major wins, all in the early 80s. She won 1 each at the du Maurier Classic (1981), the LPGA Championship (1982), and the US Open (1983) for a total of 3 golf majors.
More recent history: if Webb is too old for you, up-and-coming Hannah Green became the third Australian to win a women's golf major when she took home the 2019 Women's PGA Championship trophy, her first of hopefully more to come.
Canada:
Most titles: Canada's two women's golf major winners are split between two one-hit-wonders to date. Sandra Post won the LPGA Championship in 1968 in playoff fashion, then Canada endured a 48-year drought in women's golf (alleviated quite a bit by Mike Weir winning the Masters in 2003) before Brooke Henderson claimed the Women's PGA Championship in 2016. And of course, that one also came in playoff fashion.
China:
Most titles: China's one women's golf title came thanks to Shanshan Feng at the 2012 LPGA Championship. Finding herself down 3 strokes before the final day, Feng mounted a comeback and won by 2 strokes. She has yet to win again though has had a couple of 2nd place finishes at the 2014 US Open and the 2019 Evian Championshio.
England:
Most titles: Laura Davies made a name for herself in the late 80s and 90s with 4 major wins. She began with a 1987 US Open win after a 3-man playoff, then took home the LPGA Championship in 1994 and 1996 and then the du Maurier Classic in 1996. Prior to the likes of Sörenstam, Webb, and Park, she was the most successful non-American women's golfer. Amazingly, I think she's still playing today.
Runner-up: three other Englishwoman have won once. Alison Nicholas was the first with a 1997 US Open win. This was followed by Karen Stupples who gave the English crowd much to cheer for by winning the 2004 British Open. The up-and-coming Georgia Hall is the most recent winner, also giving the home crowd much to celebrate for at the 2018 British Open.
France:
Most titles: while France is still waiting for their first men's golf major champion since the early 1900s, two female golfers alleviated the wait just a little bit since then. Catherine Lacoste surprised the field in the 1967 US Open. Despite finishing +10, she still managed to win by 2 strokes. The more modern winner would be Patricia Meunier-Lebouc who claimed the 2003 Nabisco Championship, this time with a more conventional -7.
Japan:
Most titles: Japan has two women's golf major winners and each has won once. Hisako Higuchi became the first golfer, man or woman, from Asia to win a golf major in the 1977 LPGA Championship, winning by 3 strokes. More recently, Hinako Shibuno broke a 42-year wait for Japanese golf fans when she won 2019 British Open by shooting a -18. That was notable since it was Shibuno's first ever golf major. Hopefully she can keep it up.
Mexico:
Most titles: Lorena Ochoa is the obvious pick here, as she has both of Mexico's 2 golf major championships. She began by wowing the crowd at the 2007 British Open before following that up with the Nabisco Championship in 2008. I think it's a shame she retired so young, but from what I remember, she essentially said that she thought she had achieved all of her childhood goals in golf and simply wanted to start a new chapter in life. I can respect her for that, and she already made her name known in the women's golf world.
New Zealand:
Most titles: Lydia Ko put New Zealand on the women's golf world as she claimed the 2015 Evian Championship shooting a -16 and later took the Poppie's Pond jump at the 2016 ANA Inspiration after edging out tight competition, bringing her trophy case to 2. Mind you, she was still a teenager during both of these wins. Ko has sort of fallen off a bit since then but these two titles are still very much worth savoring.
Norway:
Most titles: Suzann Pettersen is the only Norwegian golfer to have won a women's golf major and she did so 2 times. The first came 7 years after turning pro at the 2007 LPGA Championship; beating out Karrie Webb by one stroke only added to the sweetness of that victory. She then took advantage of the newly-added Evian Championship to the list of women's golf majors by winning the inaugural edition in 2013 over a young Lydia Ko. She retired last year.
Scotland:
Most titles: while Scotland waits for its next male golf major winner, Catriona Matthew alleviated the wait just a bit by winning her one and only major to date at the 2009 British Open. I'm not sure if you can call this a nice home win considering how distinct England and Scotland see each other (the course was in England), but it was definitely a win to celebrate. She hasn't had the same success since, but there's still time for another.
South Korea:
Most titles: Inbee Park absolutely. She is the best of the best of the South Korean revolution in women's golf. She is one of the few female golfers to hold a career Grand Slam if you count her Evian Championship the year prior to it becoming a golf major (honestly, the Evian Championship has a ways to go before it reaches the status of the others). Park's 7 major wins (ANA Inspiration in 2013, Women's PGA Championship in 2013, 2014, and 2015, US Open in 2008 and 2013, and British Open in 2015) tie her for second among non-Americans behind only Annika Sörenstam. She had her best year in 2013 when she won three majors and has usually been quite dominant in her wins and clutch where need be.
Runner-up: while Park may be the best of the South Koreans, it was Se Ri Pak who began the South Korean revolution, taking 1998 by storm with 2 major wins in the LPGA Championship and the US Open. She proceeded to win the inaugural British Open (as a major) in 2001 and add two more PGA Championships in 2002 and 2006 to bring her total to 5. Pak's victory over Karrie Webb in 2006 had the unintentional effect of allowing fellow countrywoman Inbee Park to tie for 2nd among non-American golfers (rather than 3rd).
Sweden:
Most titles: no one else but Annika Sörenstam, the best non-American golfer with 10 major titles and arguably the golfer to truly spark the international revolution among women's golf that has lasted to this day. Due to the recent complicated history of women's golf majors, Sörenstam holds a career Grand Slam by some metrics (the du Maurier Classic was discontinued and the Evian Championship is a very recent addition). Sörenstam broke onto the scene with back-to-back US Open wins in 1995 and 1996 and continued to make her name known at the Nabisco Championship (2001, 2002, and 2005), LPGA Championship (3-peat from 2003-2005), and British Open (2003) before closing it out where it began, winning the 2006 US Open.
Runner-up: fellow countrywoman Anna Nordqvist may not be as successful as Sörenstam but she still has two major championships. The first came just a year after she turned pro at the 2009 LPGA Championship and the second came 8 years later at the 2017 Evian Championship. On an interesting note, Sörenstam was an Arizona Wildcat and Nordqvist was an Arizona State Sun Devil. I highly doubt there's any ill will between the two in this regard, however.
Taiwan:
Most titles: Taiwan has 5 women's golf major wins and all of them belong to Yani Tseng, who was a big name from the late 2000s to early 2010s. Tseng's rise began when she won the 2008 LPGA Championship playoff in 2008 and since then, she has added the 2010 Nabisco Championship, the 2010 and 2011 British Opens, and the 2011 LPGA Championship. That 2011 LPGA Championship was notable for her shooting a -19 and winning by 10 strokes. Tseng hasn't exactly been the same since 2011 but she's still among one of the most successful in history.
Thailand:
Most titles: the southeast nation was put on the map after Ariya Jutanugarn took the women's golf world by storm with a -16 at the 2016 British Open to win her first at just 20 years old. She followed that up with a US Open win in 2018 in playoff fashion after Kim Hyo-joo pulled off a furious comeback from 6 strokes down to tie late. This brings her total to 2 wins, and hopefully she's not done yet. She is also the only golfer, man or woman, from Southeast Asia to win a golf major.
Uruguay:
Most titles: way back then, a woman named Fay Crocker won the 1955 US Open and later the 1960 Titleholder's Championship (the only non-American golfer to have won that major) to bring home 2 golf majors, the only ones from South America in the women's world of golf. Crocker finished +15 in both majors, but considering the fact that women's golf was still in development at the time, that's not bad at all.
Women:
Australia:
Most titles: the great Karrie Webb who won 7 between 1999-2006. Webb has a career Grand Slam (Nabisco Championship in 2000 and 2006, LPGA Championship in 2001, US Open in 2000 and 2001, du Maurier Classic in 1999, and British Open in 2002). Her signature moment of dominance came in the 2000 Nabisco Championship where she won by a whopping 10 strokes. This was followed up by an 8-stroke victory at the 2001 US Open. She rounded out her career by beating up-and-coming Lorena Ochoa in a playoff in 2006.
Runner-up: Jan Stephenson was one of the few non-American golfers prior to the 90s to have multiple golf major wins, all in the early 80s. She won 1 each at the du Maurier Classic (1981), the LPGA Championship (1982), and the US Open (1983) for a total of 3 golf majors.
More recent history: if Webb is too old for you, up-and-coming Hannah Green became the third Australian to win a women's golf major when she took home the 2019 Women's PGA Championship trophy, her first of hopefully more to come.
Canada:
Most titles: Canada's two women's golf major winners are split between two one-hit-wonders to date. Sandra Post won the LPGA Championship in 1968 in playoff fashion, then Canada endured a 48-year drought in women's golf (alleviated quite a bit by Mike Weir winning the Masters in 2003) before Brooke Henderson claimed the Women's PGA Championship in 2016. And of course, that one also came in playoff fashion.
China:
Most titles: China's one women's golf title came thanks to Shanshan Feng at the 2012 LPGA Championship. Finding herself down 3 strokes before the final day, Feng mounted a comeback and won by 2 strokes. She has yet to win again though has had a couple of 2nd place finishes at the 2014 US Open and the 2019 Evian Championshio.
England:
Most titles: Laura Davies made a name for herself in the late 80s and 90s with 4 major wins. She began with a 1987 US Open win after a 3-man playoff, then took home the LPGA Championship in 1994 and 1996 and then the du Maurier Classic in 1996. Prior to the likes of Sörenstam, Webb, and Park, she was the most successful non-American women's golfer. Amazingly, I think she's still playing today.
Runner-up: three other Englishwoman have won once. Alison Nicholas was the first with a 1997 US Open win. This was followed by Karen Stupples who gave the English crowd much to cheer for by winning the 2004 British Open. The up-and-coming Georgia Hall is the most recent winner, also giving the home crowd much to celebrate for at the 2018 British Open.
France:
Most titles: while France is still waiting for their first men's golf major champion since the early 1900s, two female golfers alleviated the wait just a little bit since then. Catherine Lacoste surprised the field in the 1967 US Open. Despite finishing +10, she still managed to win by 2 strokes. The more modern winner would be Patricia Meunier-Lebouc who claimed the 2003 Nabisco Championship, this time with a more conventional -7.
Japan:
Most titles: Japan has two women's golf major winners and each has won once. Hisako Higuchi became the first golfer, man or woman, from Asia to win a golf major in the 1977 LPGA Championship, winning by 3 strokes. More recently, Hinako Shibuno broke a 42-year wait for Japanese golf fans when she won 2019 British Open by shooting a -18. That was notable since it was Shibuno's first ever golf major. Hopefully she can keep it up.
Mexico:
Most titles: Lorena Ochoa is the obvious pick here, as she has both of Mexico's 2 golf major championships. She began by wowing the crowd at the 2007 British Open before following that up with the Nabisco Championship in 2008. I think it's a shame she retired so young, but from what I remember, she essentially said that she thought she had achieved all of her childhood goals in golf and simply wanted to start a new chapter in life. I can respect her for that, and she already made her name known in the women's golf world.
New Zealand:
Most titles: Lydia Ko put New Zealand on the women's golf world as she claimed the 2015 Evian Championship shooting a -16 and later took the Poppie's Pond jump at the 2016 ANA Inspiration after edging out tight competition, bringing her trophy case to 2. Mind you, she was still a teenager during both of these wins. Ko has sort of fallen off a bit since then but these two titles are still very much worth savoring.
Norway:
Most titles: Suzann Pettersen is the only Norwegian golfer to have won a women's golf major and she did so 2 times. The first came 7 years after turning pro at the 2007 LPGA Championship; beating out Karrie Webb by one stroke only added to the sweetness of that victory. She then took advantage of the newly-added Evian Championship to the list of women's golf majors by winning the inaugural edition in 2013 over a young Lydia Ko. She retired last year.
Scotland:
Most titles: while Scotland waits for its next male golf major winner, Catriona Matthew alleviated the wait just a bit by winning her one and only major to date at the 2009 British Open. I'm not sure if you can call this a nice home win considering how distinct England and Scotland see each other (the course was in England), but it was definitely a win to celebrate. She hasn't had the same success since, but there's still time for another.
South Korea:
Most titles: Inbee Park absolutely. She is the best of the best of the South Korean revolution in women's golf. She is one of the few female golfers to hold a career Grand Slam if you count her Evian Championship the year prior to it becoming a golf major (honestly, the Evian Championship has a ways to go before it reaches the status of the others). Park's 7 major wins (ANA Inspiration in 2013, Women's PGA Championship in 2013, 2014, and 2015, US Open in 2008 and 2013, and British Open in 2015) tie her for second among non-Americans behind only Annika Sörenstam. She had her best year in 2013 when she won three majors and has usually been quite dominant in her wins and clutch where need be.
Runner-up: while Park may be the best of the South Koreans, it was Se Ri Pak who began the South Korean revolution, taking 1998 by storm with 2 major wins in the LPGA Championship and the US Open. She proceeded to win the inaugural British Open (as a major) in 2001 and add two more PGA Championships in 2002 and 2006 to bring her total to 5. Pak's victory over Karrie Webb in 2006 had the unintentional effect of allowing fellow countrywoman Inbee Park to tie for 2nd among non-American golfers (rather than 3rd).
Sweden:
Most titles: no one else but Annika Sörenstam, the best non-American golfer with 10 major titles and arguably the golfer to truly spark the international revolution among women's golf that has lasted to this day. Due to the recent complicated history of women's golf majors, Sörenstam holds a career Grand Slam by some metrics (the du Maurier Classic was discontinued and the Evian Championship is a very recent addition). Sörenstam broke onto the scene with back-to-back US Open wins in 1995 and 1996 and continued to make her name known at the Nabisco Championship (2001, 2002, and 2005), LPGA Championship (3-peat from 2003-2005), and British Open (2003) before closing it out where it began, winning the 2006 US Open.
Runner-up: fellow countrywoman Anna Nordqvist may not be as successful as Sörenstam but she still has two major championships. The first came just a year after she turned pro at the 2009 LPGA Championship and the second came 8 years later at the 2017 Evian Championship. On an interesting note, Sörenstam was an Arizona Wildcat and Nordqvist was an Arizona State Sun Devil. I highly doubt there's any ill will between the two in this regard, however.
Taiwan:
Most titles: Taiwan has 5 women's golf major wins and all of them belong to Yani Tseng, who was a big name from the late 2000s to early 2010s. Tseng's rise began when she won the 2008 LPGA Championship playoff in 2008 and since then, she has added the 2010 Nabisco Championship, the 2010 and 2011 British Opens, and the 2011 LPGA Championship. That 2011 LPGA Championship was notable for her shooting a -19 and winning by 10 strokes. Tseng hasn't exactly been the same since 2011 but she's still among one of the most successful in history.
Thailand:
Most titles: the southeast nation was put on the map after Ariya Jutanugarn took the women's golf world by storm with a -16 at the 2016 British Open to win her first at just 20 years old. She followed that up with a US Open win in 2018 in playoff fashion after Kim Hyo-joo pulled off a furious comeback from 6 strokes down to tie late. This brings her total to 2 wins, and hopefully she's not done yet. She is also the only golfer, man or woman, from Southeast Asia to win a golf major.
Uruguay:
Most titles: way back then, a woman named Fay Crocker won the 1955 US Open and later the 1960 Titleholder's Championship (the only non-American golfer to have won that major) to bring home 2 golf majors, the only ones from South America in the women's world of golf. Crocker finished +15 in both majors, but considering the fact that women's golf was still in development at the time, that's not bad at all.