Greenday has catchy tunes, and that's all you need to be well known. Personally, there's something I don't like about them. Maybe it's the fact there like like 40 year-olds, yet they dress up like emo kids - maybe that's it.
Below are some of my favorite rock/punk/alternative bands:
Red Hot Chilli Peppers
Guns N' Roses
The All American Rejects