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I have a fair number of imports from both the US and JP, since I'm a PAL gamer. Mostly handheld games, but also have some PS2 stuff.

perfect dark for the n64 was my first import, nintendo did not release it here in germany back in the days

Azure Dreams

My imported PS1 games (JAP):

Penny Racers, J.League Jikkyou Winning Eleven 3, Option Tuning Car Battle, Ultraman (I cannot remember which game exactly), Street Fighter Zero 3, Tekken 2+3, Jojo's Bizarre Adventure, Super Gem Fighter, Mega Man X, King of Fighters '97, Fatal Fury: Wild Ambition, Winning Eleven 3: Final Version, Winning Eleven 3: World Cup France '98, Winning Eleven 4, Street Fighter EX2 Plus, Bio Hazard Survivor (gun shooter), Dino Crisis.

I've owned many more imports for other consoles, but the PS1 stuff is what I remember best.

My first import was the Sailor Moon SuperS fighting game for PS1. Was kinda fun if a bit silly.

Outside of that, mostly PSP and DS games because I don't feel like modding another console. And two PC games since my PC doesn't require mods either.

PSP games I've imported: Tales of Destiny 2, Tales of Rebirth, Ys vs. Sora no Kiseki Alternative Saga, Tales of Eternia (European version)

PC games I've imported: Sora no Kiseki SC and Sora no Kiseki the 3rd.

DS games I've imported: Tales of Innocence, Tales of the Tempest.

All Japanese versions except Tales of Eternia since the PSP version never came to the US and I prefer to play on handhelds. I'd import more, but my ability to read Japanese is laughably bad at best. I can read katakana and hiragana, but only know a few random kanji (and really random ones at that, it's obvious what little I know comes from playing RPGs).

Dynasty Warriors 7 Xtreme Legend for Steam

999 for the DS

Man, I haven't imported any games since the days of the original PlayStation.

Oh wait, I did import several Dreamcast games (mostly shmups) as support for that console died off.
I also have a collection of games from the "16-bit era", but they're not "imports" since I lived overseas at the time.

What do you mean by imported?

Diablo 3 and BF3 from the UK

Best game I've ever imported is Osu! Tatakae! Ouendan.

Saints row 2 because the German Version is Low violence

I used to play a few on my original playstation using the open lid disc swapping spring trick thing but I never actually owned those games. My mate used to buy them from CEX (a shop in UK). I remember him trying to struggle through the first Parasite Eve with a printed off poorly translated script.
Me though, the only thing I import is music.

Football Manager 2014 and Dead Island. They are not distributed in Germany. FM 2014 because of license Issues for the German football leagues and national team. Dead Island is not distributed here, because the Publisher knew it never would have get a rating from USK (Unterhaltungssoftware Selbstkontrolle - entertainment software selfcontrol) and so it would have to be sold only to people 18+ without any advertisement. Even the box standing in shelf in a regular shop is advertisement. So you have to prove in the Shop with your ID-Card that your are 18+ and then you could get the game from under the cash desk.

Final Fantasy Tactics

If you mean by imported: bought by a shop in another country or via trading with a foreigner: then my list is shorter the other way around: everything on my account except:
Arma II: Combined Operations (ROW)
Torchlight II
Anno 2070 - Deluxe
System Shock 2
Fallout New Vegas Ultimate
Counter-Strike: Global Offensive
Day of Defeat: Source
Mass Effect 2 - Digital Deluxe
Audiosurf
GTA IV Complete Bundle
Dota 2 - Hardware Survey
Nexuiz
Team Fortress 2 - In-Game Upgrade (DE)
some DLCs
Why? Regional restrictions for Germany and stupid pricing. Even my first game was Skyrim (UK)...

Kingdom Hearts 2 Final mix.