A lot of my favorites have already been listed as well, but I'll add a few more I can think of off the top of my head...
Propagandhi - Older stuff is best, but newer stuff is still good.
TSOL - Make sure it's the band's original lineup (albums Thoughts Of Yesterday, Dance With Me, Beneath The Shadows, I Disappear)
88 Fingers Louie - They broke up a while ago, but if you can get your hands on Behind Bars, its one of the best punk albums I think.
Pinhead Gunpowder - Very similar to Green Day's first couple albums, mainly cuz Billie Joe is in the band
Operation Ivy - I can't believe no one's listed them yet...
Face To Face - Older stuff only...anything after their self-titled album is a waste of time IMO.
Fifteen - Really great stuff, Jeff Ott puts his soul into his music.
Avail - Hardcore punk rock with some dixie influences.
J Church - Really hard to describe, I don't like all their stuff but most of it is pretty good.
Strung Out - Skate-punk similar to Pennywise and Face To Face.
Mindless Self Indulgence - Not purely punk rock, heavy industrial influences, but they're great to listen (just make sure you have a sense of humor if you do!)
Bouncing Souls - Great music, don't take themselves too seriously, songs like "These Are The Quotes From Our Favorite 80s Movies".
Snuff/Guns N Wankers - Really unique sound, can't think of another band like them.
Tilt - Again, try to stick with their older stuff. Their first album (Play Cell) was their best.
Other favorites already listed include...
Crass (definitely an acquired taste, as noted above)
The Damned (great stuff, varies between really gothic tunes and hardcore punk)
Subhumans (agree with the poster above, one of the best bands ever)
Agent Orange
Pennywise
Rancid (first two albums)
NOFX
Dead Kennedys