simulation: Ace Combat, Animal crossing, Harvest moon.
Harvest Moon is a niche title, not a major seller.
None of them are near the most successful games of the genre, which include SimCity, The Sims, and Microsoft Flight Simulator.
Sports: Gran turismo. Most sports games are nation specific, I have never played any NFL or NBA game.
GT is a racing game - I said sports in general. In particular, it's a racing simulator - and it's really the only racing simulator that can compete with arcade racers like Need for Speed (made in Canada and England), the Cruisin' series (made in America), Midnight Club (also American), and Ridge Racer (Japanese).
The most widely-played sport in the world is soccer (or association football for all you non-Americans) - the soccer video game market is led by EA's FIFA franchise, followed closely by Konami's Pro Evolution franchise.
MMO: Everquest, FFXI
FFXI is, sadly, not very influential. And not among the most successful MMOs.
Everquest was made in America. The San Francisco Bay Area to be exact.
As far as MMOs goes, Japan can't even compete with (the much less populated) South Korea, let alone the US or China.
Adventure: Legend of zelda. Though Adventure is an overshadowing genre; RPGs, platformers, MMOs can all be considered adventure games.
No, they can't; adventure is a distinct genre from RPG, action (which is what platformer is a sub-genre of), and action-adventure (which is what Zelda is, and thus why Zelda doesn't count).
Adventure games are things like Zork, Maniac Mansion, King's Quest, Leisure Suit Larry, Myst, Monkey Island, Heavy Rain, Shadowgate, and so on.
Japan only dominates the sub-genres of dating sims and visual novels, both of which have virtually no presence outside of Japan and are therefore nearly irrelevant.
I wouldn't say puzzle games are really dominated either way.
You just agreed with me. I did not actually say that they were; those genres I listed were ones that Japan could not believably be said to "dominate". That does not imply that some other country does dominate.
That being said, it's worth noting that by far the single most influential, most widely played, most frequently ported, most often ripped-off puzzle game of all time was made in Russia.