Some of my personal favorite hidden gems:
Eternal Ring (PS2) - This game was I believe a launch title for the PS2, and as we all know, PS2 launch titles tend to be pushed aside for their questionable quality. In this games case though, it is absolutely incredibily addicting. Think of King's Field, only set in a more interesting world (lots of different places to explore rather than a boring monotonous dungeon). The game also puts more emphasis on Magic use, which you use magic by crafting magic into rings using stones representing the elements, with a tier system of stones for each element. It's classic first person RPG action at it's best, almost completely nonlinear, a story that keeps you going from one area to the next, and addicting magic system. I give this an 8/10
Extermination (PS2) - This game came out pretty early in the PS2's life, and was supposed to be a killer of Resident Evil as far as survival horror champion, and it should have too. At the time this game came out, Resident Evil was still a slow paced survival horror with tank controls. Extermination gave you full 3D control of your characters, and plenty of ammo to keep the action interesting, but not enough to make it feel easy. The game itself takes you through a base at the North Pole (or somewhere around there) that has been infested by a life form that evolves as you move through the game. I thought that the evolving life was very innovative at the time, as was the main character's gun, which could go from being a machine gun, to a flamethrower, to two other guns I can't remember for the life of me. The knife was actually usable in this game unlike the early Resident Evil games. I give this an 9/10
Breakdown (Xbox) - Probably the best game on this entire list, is also probably the least well known. Breakdown was quite literally a breaking experience, bending the perception of what we came to expect in FPS games. The game had some extremely interactive environments, which were rare at the time. The main character himself had to use his mind to alter the playfield, and at the same time, the game wasn't 100% nonstop shooting like most FPS. The story in Breakdown is among my favorites ever, basically beginning you in a prison facility you had no recollection of, and you searching for what happened. I give this an 10/10
All I can think of for now