I'm a big Green Day fan myself. I particularly like American Idiot because I'm a sucker for musicals and rock operas XD I've loved pretty much all their CDs (After Dookie, because I'm not much into punk - although I LOVED "Who Wrote Holden Caulfield?") and eagerly await their next one. Great band, Billie has a stunning voice and a real way with words =D I adored the song they did with U2 ("The Saint Are Coming").
Personally, my favorite song of their's is the extremely underappreciated "J.A.R. (Jason Andrew Relva)". Brilliant song, brilliant lyrics.
I saw them in concert 2 years ago and it was simply amazing. I was across a football field from them but oh well XD They really know how to pump up a crowd.