If what you're looking to do is introduce a new person to Punk, there are several more modern variations you can use as kind of a feeder to get them to understand the older bands, and these are:
-Street Punk
-Ska Punk
-Punk Rock/ Pop Punk
A few examples of each include:
Street Punk- The Briefs, Anti Flag, The Bastards
Ska Punk- Less Than Jake, Mighty Mighty Bosstones, Rancid, some older No Doubt
Punk Rock/Pop Punk- Sum 41, Bowling for Soup, Green Day
Once you've got them hooked, you can stop worrying so much about genre restrictions and go all out. At the next stage, you may still want some mainstream recognition, but you don't have to worry about as mainstream a sound any more, so some bands I would recommend:
Bad Religion, Pennywise, Flogging Molly, Millencollin, Offspring, Sublime, etc.
Oh God, this part made me want to cry. This is like a correction they publish in the paper when people fuck up with someone's obituary or something:
Ska-Punk: MU330, The Chinkees, The Toasters, Planet Smashers, KING APPARATUS, The Johnstones.
Pop-punk/"Contemporary Punk": Descendents, The Methadones, Alkaline Trio, The Riverdales, The Broadways, The Lawrence Arms, Teenage Bottlerocket, Screaching Weasel, later Jawbreaker, Hot Water Music.
Dance/Noise-punk: Les Savy Fav, Drive Like Jehu, Q and not U, The Jesus Lizard.
Alt-punk/Awesomeness: Jawbox, Shellac, Rye Coalition, McLusky, Pitchfork, Shiner, Unwound, Burning Airlines, The Honor System.
Blank-core: The Bronx, Blood Brothers, early Thrice, Small Brown Bike.
80's punk: Cramps, The Dwarves, Misfits, The Jam, 7 Seconds.
EDIT: Also, am I the only lady commenting in this thread??
I leave on this note: Dudes! Pop-punk can be great! Don't follow the lameness of mainstream media's interpretation of one of my favourite genres!
