What kind of music do you think the Futurama characters like? Here's my 2 cents:
Fry - 80's and 90's, and some rap. He'd like those one-hit wonder 80's bands. And the 90's bands he'd like would probably be Reel Big Fish, Green Day, Blink 182, and The Bloodhound Gang.
Leela - Hard core alternative punk rock!Goes well with her angry personality! She'd like Nirvana, Smashing Pumpkins, Pearl Jam, Korn, Linkin Park, STP, Soundgarden, Bush, AFI, and Arcade Fire.
Bender - Classic Rock! Eric Clapton, Led Zeppelin, The Ramones, Sex Pistols, The Stooges, Rolling Stones, The Doors, ELO, Bachman Turner Overdrive, Blue Oyster Cult, and Emerson Lake and Palmer and T-Rex.
Hermes - Anything reggae like Wayne Wonder.
Amy - Girl pop singers like Christina Aguilara, Ke$ha, Britney, and the whatnot.
Zoidberg - Boy bands! Like The Backstreet Boys, N-Sync, Jonas Brothers, and Jesse McCarthy.