Black Flag
Ramones
TSOL
SNFU
Dead Kennedy's
Bad Brains
Descendents
Minor Threat
I think Punk was in its heyday in the 80's. I think its evolved over time and many people don't believe "pop punk" is really considered "punk" even though a lot of the themes we saw in the 80's punk bands are very clear and present in Green Day's music.
Which then begs the question what really defines punk music? I'm honestly not sure because many of the hallmarks of the 80's punk was the poor production, guitars out of tune, singers who couldn't sing very well - all of which have been greatly improved when you consider Green Day's music.
Billy Joe Armstrong is a phenomenal singer. Even on Dookie, the producer said a majority of the songs he did in a single take - which is staggering to think about. Their musical abilities are unquestionably much better than any of the 80's punk bands. Tre Cool's drumming is just on another level and I'm not sure many 80's era punk band drummers could ever hang with his abilities. Even the production level of Dookie was light years ahead of many of the seminal punk albums that came out in the 80's.
Its easy to claim that Green Day isn't a "real" punk band, but when you start to compare them to the "prototypical" bands in the 80's, they sing about many of the same things, but have elevated the genre beyond what its really been known for. In the end, I have a harder time not calling them punk, there's just too many similarities to many of the most popular bands people know.