I like too many different kinds of music to list here.Quite literally every style aside from complete death metal, dubstep (with some exceptions), and much of modern pop (nooo J-Biebs please). Of course there are some specific artists/songs which I dislike, but no kind of music I don't. Obviously I can't have every song ever in iTunes, so I have to be selective. Many styles I like have already been listed here, as have a LOT of my favorite bands, so I'll just post some things that I don't think have been posted yet:
Avantasia is a fantastic power metal project with tons of variety because of the continually changing instrumentalists and multiple vocalists. IF you like Dragonforce you should look into this band, I think they have some similar stuff (though I don't listen to much Dragonforce).
This one's really long, but trust me patience is worth it
There seems to be a terrible lack of jazz in this thread, so... Squirrel Nut Zippers are awesome
and so are the Budos Band (found them from Sleeping Dogs)
I love the band Turisas
Black Moth for people who like Grunge... Or whaveter, just listen
and of course Yes
The list could go on... and on... and on... and on, but I've probably already posted too many videos... sorry.