I listen to a wide variety, but alt rock is at the top of the list. Tool, Red Hot Chili Peppers, Pearl Jam, Natalie Merchant, The Cure, REM, Blind Melon, Bad Religion are my top picks. And I recently started listening to George Hrab's music, good stuff.
If it has meaningful social commentary, I'll listen to it. If it's nerdy, funny, or sciencey I'll listen to it (They Might be Giants, Weird Al, anything Monty Python). Mostly I listen to punk, ska, rockabilly, Nueva Trova, reggae roots, some metal, and alt./indie rock. I can't stand rap, hiphop, and the worst of the worst: reggaeton.
For your listening pleasure: Jonathan Coulton sampler. I recommend them all, but I'd start with Mandelbrot Set if you like math, Chiron Beta Prime if you like post-apocalyptic scenarios merged with those dreadful Xmess letters people send out at the end of the year, or Re: Your Brains if you've ever wondered what would happen if that jackass at the office suddenly became a zombie.