They are ok, I like basket case, american idiot, time of your life and some more I cant remember the name of.
I think Green Day is one of my top 5 favorite bands. I knew I wanted to play guitar after I watched the video for "Basket Case" on MTV when I was 12. Their old stuff is so energetic and raw, and that's what I like to remember about them. I will listen to any tune from their first four albums ( 1039... Hours ---> Insomniac ) The tunes I would sit and listen to from the rest of their catalog though are few and far between - Nice Guys Finish Last, Jinx, Reject, Scumbag, and Ha Ha You're Dead. However, I DO commend them for sticking together, unlike most of my favorite bands that have had to trudge through difficult line-up changes ( Ahem, Megadeth...! :-\ )
I brought their greatest hits a few years back. It was an excellent purchase in terms of listen-to-skip ratio. Their newer stuff doesn't really appeal to me, although I like Holiday and Jesus of Suburbia.