I hope this post kind of renews your faith in punk being alive and well. Remember, "punk music" is a really broad term that encompasses many different subgenres, just like any general genre, like rock, metal or classical. I'm also including bands that have the punk mentality:
Amen - punk/metal hybrid, one of my personal favourites, actually.
Leftover Crack - A ska/crust punk hybrid. Also quite good, though they may have broken up last year. I'm not sure.
Morning Glory - Another ska punk type band with some members from Leftover Crack.
The (International) Noise Conspiracy - The singer from Refused (amazing band but broken up) decided to make situ-inspired garage rock.
Behind Enemy Lines - Crust/thrash punk/metal band. (Even though they broke up in 2001, try Aus Rotten, as well)
Dystopia - 9 Slude/metal/punk.
Against Me! - They were folk punk (Reinventing Axl Rose, great album) but now they're different, but still punk rock.
And you already said them but I'm getting more and more into Rise Against.


And if you're really in the mood for reading, then this thread on Something Awful is good.
Punk/Hardcore/Emo megathread: pre-gaming for Fest 7 - The Something Awful Forums
You can find some punk bands in there.

Honestly, just find a genre of punk you like (to which there are many) and go to wikipedia and look at a list.