Great thread. +1 for AFI, Strung Out, The Misfits, None More Black, Hot Water Music, Defeater, Rancid, A Wilhelm Scream, Minor Threat, Fugazi and likely more I'm failing to recall now.
If you like None More Black, Kid Dynamite is required listening. Jason's (lead singer) prior band. Bandmate Dr Dan Yemim was also in Lifetime and Paint It Black, two other excellent bands.
If you like Hot Water Music, check out The Draft. Basically HWM sans Ragan but still good.
If you like Defeater and Modern Life Is War, you'll like Stay Gold, Crime In Stereo, and Sinking Ships. Probably also Blacklisted.
AZ bands of old people should be familiar with outside of the Meat Puppets (but not closely related): Where Eagles Dare, Hour of the Wolf, Run With the Hunted, and Life In Pictures (more metalcore but dudes ripped and went on to form Hour of the Wolf so kudos).
Ceremony is another great band although their sound has changed over the years. Also, Fucked Up has some solid releases. Hidden World is an incredible album and their most recent is just as good.
When it comes to punk crossing into crust and d-beat, I fucking love Tragedy. Disfear is good too (mainly because Tomas Lindberg is the man) but Tragedy, good lord.
I'm sure I'll think of more later on.
