Osu! Tatakae! Ouendan & Elite Beat Agents on the Nintendo DS. 
You've got loads of Japanese rhythm arcade games as well.
Vib Ribbon, Bust-a-Groove and Gitaroo Man are other games where the gameplay is directly derived from the music.
Shadow mentioned things like Dance Dance Revolution and the thousands of other games that followed in his wake. But maybe Audition Online deserves a mention for breaking the mold somewhat - it's also a MMO.
If you could be more specific about what you're looking for it could help. A lot of games use music as a kind of feedback or reward (Ex: Super Mario World's Yoshi), or as en excellent tool for suspence and horror (Silent Hill without the music would suck).
PaRappa the Rapper for ps1 of course, think it was the first advanced one for the console of its kind
But also music in all games in very important in creating an immersive experience, it can really make or break the game, so I'd make sure you touch on that somewhat
Mario Paint for the super nintendo enabled you to have a mouse and make your own songs 
I would check out games like Gothic 3. I read a pretty interesting article from Kai Rosenkrantz (in german) where he told how they had the gameplay sourrunded by the fitting music with data sets in theyr soundtrack wich allowed the game to mix the various themes and tracks depending on how you play and what scene you are experiencing.
what about Rez
Quote from zaphodwhat about Rezhttp://en.wikipedia.org/wiki/Rez
lol...forgot about this one. Rez gets an A+ for innovative use of music.
thats the only reason I remembered it
....well yeah...exactly. 
I think SharCry should be on the list even though it's an indie. It's a game where you control your character purely with a microphone and your voice. It's a really fun experience in multiplayer when you are 50+ people.
Quote from Sentura
Wow, and us guys are labeled as weird gamer geeks :roll:
Quote from Sentura
Hahaha, funniest thing I've read in ages.
i almost forgot, jam session for the DS
There was a game named "music" for the original PS, but i don't think that's what you're looking for
But who honestly didn’t think “Sod trying to boost Quetzalcoatl, I’m going to see if I can get this oscillating against my prostate”
... err
Don’t have an account yet? Register yourself now and be a part of our community!
