Video Game Music
I would like to start by pointing out VGMusic.com. In my opinion the best Video Game Music site, and can provide a great source of Music. That being said, you can also find mostly what you need, right here. Apart from Zelda, each zip contains a small amount of .MIDs that passed my quality test. Enjoy!

Final Fantasy
Mario
Halo
Sonic
Other or Unknown
Zelda
Zelda is bold as I have managed to locate nearly every Zelda .MID out there with most of the music (to my knowledge) Of Link's Awakening, Minish Cap, Oracle of the Ages/Seasons, Majora's Mask, Ocarina of Time, Twilight Princess, Spirit Tracks and Phantom Hourglass. With a couple of extra golden treats ;).