Brigandine: Grand Edition for PSX. Brigandine Legend of Forsena was localized for the US. Grand Edition follows the exact same storyline, but the game has updated graphics, 2D sprites attack in battle instead of going 3D. There are a few pretty major changes to how the game plays. There's also an actual last boss in the game, while the original Brigandine had it in the storyline, once taking over the continent that was it. Many classes have spell changes, spells have different effects, certain story characters are given special classes, my favorite monster class is given an upgrade to rank three, etc.
Beavis and Butthead Virtual Stupidity for PSX. This game was released on the PC in the US, but on the PSX it was released exclusively in Japan? Why? This is an adventure game similar Police Quest, Monkey Island, Leisure Suit Larry, etc. It's actually a very good game, and a lot of the charm to the game is actually trying everything out that you can do rather than just doing what you need to. I think it's the best Beavis and Butthead game, although with the quality of the rest of the games, anything decent would have been the best.
Mobile Suit Gundam One Year War for PS2. If you like the original Gundam "at all," you need to play this game. The game has fairly good gameplay, but it's the storyline is what really shines. Think of the original Dragon Ball Z Budokai and how much detail there was in the cutscenes when showing off the storyline, and then multiply that by ten fold. This game goes into an extreme amount of detail to carry you through every bit of the origiinal Gundam's storyline. With fairly good gameplay and how well it plays out, it's the Gundam game any fan of the original needs to play.
Gundam Battle Universe for PSP. Yes, another Gundam game. There are three games prior to Universe, but Universe has all the content that the other ones have(minor changes though such as doing a charge dash does a triple slash instead of the characters moving attack.) Now opposite from One Year War, while this game does have literally every single mission in order that you'll see in any Gundam from the original 0079 all the way up to 0093, the game doesn't have the detailed storyline. However, this game is all about the gameplay and playing as tons of mobile suits. The game has a sort of level up aspect, so if you are playing as a MS-06F Zaku 2 and complete a mission, you can put those points that you received into increase HP, Mobility, Weapons, etc, etc, A common question, is which is the better Gundam series, Gundam Battle or Gundam vs Gundam. I think anyone will get far more enjoyment out of the Gundam Battle series than the Gundam vs Gundam series because it's got great gameplay and lots of content. Gundam vs Gundam also has great gameplay, but has almost no content. Gundam vs Gundam is noob friendly and easier to get into, which is why I think a lot of people like it better, although like any fighting game, Gundam vs Gundam does technically have the better gameplay.
There are more good Gundam games that haven't been released here and that's because after the Namco Bandai merger, rarely will they release anything that won't sell huge numbers to the west. Gundam in Japan is like Dragon Ball Z everywhere. It's a highly praised franchise, so that's why there are so many actual good releases to the series. I've only listed my favorites.