We all remember the great Monkey Island songs.
We can also feel epic when fighting bosses at Halo 3 because of it's fantastic soundtrack.
So, it is clear that music is a very important component in videogames... but what about being the key component, a true determining element?
First, DDR and Stepmania appeared: Dancing on an arrow-marked mat or platform, following the on-screen music to get the feel of dancing. Easy concept, plus on Stepmania you've got hundreds of famous songs to play.
Difficulty adds additional steps, faster arrows, better precision (to detect incorrect steps), and multiple simultaneous steps. The song influences too (a Britney Spears won't have the same "dance" than a DJ Tiesto song).
Since I tried it at home, it's my way of doing aerobic exercise (but I do not play at arcades, just at home).
Then, Guitar Hero series came: Same idea of DDR but exchanging a dance mat for a joystick-guitar.
Easy to learn (at least my friends are better moving their fingers than their legs), less embarrassing if you play in a public place, and very very fun. I'm searching for another USB guitar to be able to play coop with a friend (GH2 on 360, GH3 on PC).
Recently Rock Band came out as a "second version", with additional instruments and up to four simultaneous players.
And now, another possible revolution comes from the indie development scene, Audiosurf: Load the game, choose a MP3 song, and fly in a space highway trying to align same-color blocks, everything procedural generated from the chosen song.
It is still a beta (you can only play few songs of your own, then only the demo ones) but very playable, addictive and focuses more on your reflexes than on feet/fingers music synchronization.
I can't wait for the final version to be released to buy it.
So music can be a key component, indeed. And it usually ends being a cool one :)
Note #1: I've deliberately left out Rez out of the list because I haven't played it (yet).
Note #2: To better enjoy Audiosurf, I recommend playing with joystick/pad instead of keyboard (with the 360 controller it's fantastic).