I'm just going to interpret this as a "What's your favorite band?" topic, since we already have one for favorite songs.
As far as alternative rock/pop punk/nu metal/that sort of thing goes, I used to be into it, and still listen to some on occasion. I listen to Fall Out Boy a fair amount, though I don't like much of their post-hiatus work, personally. Folie à Deux is their best album, for my money. I also quite like Panic! at the Disco (mainly their Vices and Virtues album), MCR (only their second two albums: The Black Parade and Danger Days), Green Day (mainly American Idiot and 21st Century Breakdown), Linkin Park (mainly A Thousand Suns), and AAR (mostly their latest two albums).
As for metal, I love Rush (I guess they aren't always metal, but whatever), Nightwish, Dream Theater, Queen (they aren't known for it, but some of their older work, such as Queen II, definitely qualifies as metal), Symphony X, and Blind Guardian, as well Iron Maiden and Led Zeppelin. I won't list albums since I usually like just about anything I hear from those groups. In general, I tend toward the more melodic metal subgenres; I don't care for cacophony or death growls.
I just listened to Fragile and Close To the Edge the other day! In terms of prog rock, I also love King Crimson, Genesis, Jethro Tull, Pink Floyd, Camel, and a ton of others. It's my favorite rock subgenre.