Oh goodness so many games have already been said... of the ones that haven't been listed yet:
Lost Kingdoms 2 (GC): From the makers of Dark Souls came humble beginnings, but in this game you can see the spirit of a wonderful emerging company with creativity. If anything would sell you on this game:
DARK SOULS + POKEMON = Need I say more?
Really fun game I've played so many times. Really hope FromSoftware returns to it now that Dark Souls is done.
Grandia II (Dreamcast, PS2): Oh man. The other two Grandia games are garbage, but this gem is amazing. So dang campy and it knows it. There are few times JRPGs just embrace how stupid their plots can get, and Grandia 2 does this and also adds an amazing real time, turn based hybrid battle system that many indie games have lovingly adopted (Child of Light).
The battle system is so good, you actually want to grind even though the game doesn't make you. You can even be underleveled and win a fights based on skill and strategy alone!
What?! A JRPG without grinding and no random encounters?! What you can even prevent your opponents from attacking by being smart about your timed attacks? Okay, look it's amazing. Just try it for yourself. You can buy this game on Steam pretty cheap. So give it a go!
Rayman 2 (N64, Dreamcast) : Okay this might be some nostalgia talking, but this game man. Love it to death, influenced my art style a ton, and is still my favorite childhood 3D platformer. It fixed so many flaws Super Mario 64 had, and the art was so stylized that even as an N64 game the art holds up fairly well today.
If you've got a spare few dollars go pick it up on GOG.com!