My top favorite artists are Between the Buried and Me (progressive metal), Thrice (alternative rock?), Nickel Creek (technical folk/alternative), Al di Meola (flamenco jazz), mewithoutYou (experimental rock; not counting their fourth album), and Queen (opera-pop-rock who knows).
Some genres that I like, with favorite bands from each one:
Metalcore - The Devil Wears Prada, August Burns Red, Norma Jean
Hardcore - Underoath, Maylene and the Sons of Disaster, Showbread, Sleeping Giant
Post-Hardcore - Emery, Dead Poetic
Indie Pop - The Hush Sound
Classic Rock - Journey, The Eagles
Alternative Rock - Thrice, The Almost, Death Cab for Cutie
I also like a little bit of country, with no particular favorite artists. I guess I like at least a little of everything, except j-pop, "fluff" pop (Miley Cyrus, etc.), trance, techno, rap, and hip-hop. Classical music has piqued my interest, but I haven't really checked it out much.
I also want to share this awesome quote that I found on the side of a Starbucks cup that expresses part of my opinion on music:
"Music can lift us out of depression or move us to tears -- it is a remedy, a tonic, orange juice for the ear. But for many of my neurological patients, music is even more -- it can provide access, even when no medication can, to movement, to speech, to life. For them, music is not a luxury, but a necessity."
--Oliver Sacks, neurologist