I agree that their older stuff was alot better. The American Idiot album was generally ok to me. I'm not so sure about their newest though, havn't really been keeping track. :/
I like the songs Wake Me Up When September Ends, Holiday, and Boulevard of Broken Dreams. They were all pretty catchy. Although WMUWSE used echo effects a lot..
My mom is a big fan (better than her normal, country stuff) but I'm not really. They've got a few good songs (Boulevard of Broken Dreams, American Idiot) but the rest aren't really my style.