I decided to create this thread because it was mentioned that a separate list should be created for some imports. I'll start off with some.
PS3: ( Easiest console for imports, only games locked are Persona 4 Arena, and Way of the Samurai 3 for Slim models')
Aquanaut's Holiday- Hidden Memories- Sub Adventure game that has a Hong Kong version with English/Chinese text options. Rare and expensive.
Tales of Vesperia- JRPG that is like the Xbox 360 version but with new content, and wasn't released internationally.( Apparently Japanese version also has English text as well.)
Okami- Action game that is like the PS2 and Wii versions, but in HD, and also has a Hong Kong Version with English text options.
Initial D Extreme Stage- arcade Racing game based off the manga. Gameplay is similiar to Inital D Arcade Stage 4.
Ketsui - Cool shmup with a military setting. This version is region-free compared to the X360 version, and the limited edition comes with a superplay Blu-Ray, and a 2CD soundtrack.
X360: ( Somewhat good for importing, make sure you check what games are region-free since even different editions of the same game could have different region allowness; may need a Japanese 360 to enjoy some of the better imports)
Muchi Muchi Pork/Pink Sweets Double Pack- Two Cave shooters in one package, with MMP being the better of the two games. Limited print run and pretty expensive.
Monster Hunter Frontier Online- Cool online spinoff of the Monster Hunter series.
DodonPachi Resurrection(Daifakkastu)- Another Cave shooter that can be gotten for pretty cheap, and there is a English version released in Europe for imports.
Espgaluda II/Mushimimesama Futari/Dodonpachi Saidaioujou- More Cave shooters that can be gotten at cheap prices for the regular editions. Espgaluda's II's Limited Edition is region-locked, while the LE and SLE of Saidaioujou are very expensive, because of the goodies contained inside.
Eschatos- Above average shmup thats region free and cheap.
Virtual On Cyber Troopers Force- Fighting game with mechs, and is the only port of the game from the original Sega Hikaru release. The regular edition is pretty cheap, but getting the memorial box LE and the Twin Sticks controller will be extremely expensive.
Update: Wii import suggestions can be added as well. I'll make some other import lists in the future for most generations of consoles.
Wii: (Hardest to import because of built in region lock into the console, you need to do softmoding on your Wii, or pick up a Japanese Wii(this is necessary for Dragon Quest X!)
Milestone Shooting Collection 2- Same as Ultimate Shooting Collection, but added Radirgy Noa Massive and Illvelo to the collection( Illvelo has its own Japanese release as well). Also available on the X360 as Sakura Flamingo Archives.
Captain Rainbow- Action-adventure game that apparently was going to get a translated European release, but was canceled and remained in Japan. Apparently sold terribly as well.
Monster Hunter G- Updated port of the PS2 release as an expansion to the original Monster Hunter.
Taiko no Tatsujin- Rhythm game that can be played with wii remote, classic controller, or the drum perihperal.
Tales of Graces- JRPG in the Tales series. The updated version got a international release on the PS3, but the original version is a Japan exclusive.
Fatal Frame 4- Awesome survival horror game.
428- A really good visual novel game, and also on the PS3, PSP, iOS, and Android in Japan.
Also to note is the Virtual Console library for the Wii in Japan has a much greater selection of games to pick than other regions.