I think they suck. They're just American faux punk soccer mom music.
+1
Just off the top of my head, Gaslight Anthem is a contemporary faux punk band that's way better and more interesting than Green Day. They are still a bit too manufactured for my taste, but at least there's some degree of authenticity in their repertoire.
Sonic Youth is the best thing to come out of the punk movement though, IMO. Sex Pistols, The Clash, Patti Smith, etc are all great too, but they have a limited appeal that's so obviously outdated now.