Without getting into the debate about whether or not they're punk (because I don't give two fucks about what box people want to put bands in):
Up to Nimrod: amazing.
Warning: I really liked it, in fact still do, but I can see why so many people didn't.
American Idiot: initially good, but I got tired of it quickly.
21st Century Breakdown: initially horrible, but I can just about put up with it these days.
I would dearly love for them to stop this stupid lyrical pretense and concept nonsense and go back to writing songs about... the sort of random stuff they used to write about. The change in their sound didn't bother me in the slightest, I still think they're capable of writing some great tunes, it's just the lyrical content that makes me think "yeah, no".