I'd like to mention both Ouendan games and Rhythm Tengoku. In the case of the former, it actually got a "westernized" game called Elite Beat Agents for the west that never got released in Japan. Luckily both those don't require knowledge for the Japanese language to fully enjoy, and I recommend importing both. (You can find both Ouendan cheap enough but Rhythm Tengoku is pretty rare and kinda expensive.)
Ace Attorney Investigations 2 is a big one. The first game is my favorite because of the detective focus rather than the courtroom, despite the story not being as fleshed out as the first Ace Attorney games. From what I heard the sequel is much better, but apparently I have to wait until the fan translation.
The Densetsu no Starfy games are another I'd like to mention. I'm actually pretty surprised Nintendo didn't localize any games except the latest one. It's a platformer akin to Kirby that features a cute starfish main character, I can't imagine it not doing well over in the west. Speaking of which, did the DS game do good?
There's also Hajime no Ippo for the GBA. It's a boxing game based on the anime that has similar gameplay to Punch Out, and being a fan of boxing, the anime and Punch Out as well I've always wanted to try it. I plan on importing it eventually, but would have loved for it to be localized. (Even though it obviously wouldn't have done well.)
There's also the Jake Hunter series, which is a popular long-running japanese series of detective games but only had one title localized. I've got a copy of the game not too long ago, but I've still yet to play it myself. Still, I'd have loved if other games were localized because the universe and characters are all so interesting.
There's also the likes of Mario vs Wario, Mario's Picross 2, New Play Control Chibi-Robo (shut up it still counts), the first Animal Crossing, etc.
I'd also like to mention Manzai Birds only being available to play on the japanese version of Rhythm Heaven Fever (Minna no Rhythm Tengoku.) Nintendo robbed us from the best endless game in the series! >:(
Does it have to be from Japan? I can think of games that were released in Europe but never in America, and vice versa. (Though all of them are available in Japan.)
Example:
Trauma Team, Mario Super Sluggers and ExciteBots are Wii games that are available in America but not in Europe.
Disaster and Another Code R are Wii games that are in Europe but not America.
There's also The Last Window, a DS game that is available in Europe but not America. 999 is also another DS game but was out on the opposite country instead.
The Tingle DS game were never out in America. (And the sequel is Japan only I believe.)
Warioware Twisted and Jill Dozer are big ones.
The Virtual Boy in general was never released in PAL land.