Sick of Green Day
*gasp*
Most of what I listen to falls under one of those categories. I'm too lazy to save my current playlist as an html and upload it somewhere, so I'm gonna list some specific bands:
(apologies in advance if I get genres incorrect, I was never well-versed in different styles of punk and such; I generally can tell between punk and emo, but it's all blurry)
Sum 41 - Skater punk, I guess. They remind me a lot of the Beastie Boys, if the Beastie Boys had guitars. Hell Song, Fat Lip, and In Too Deep are all goood.
Hawthorne Heights - emo. Screamo, maybe. Lots of loud whiny screams and songs about lost love and such.
I like them. I recommend Ohio is For Lovers.
Juliana Theory - JTheory was recommended to me by a friend. Their sound is kind of soft, most of the time. Get "If I Told You This Was Killing Me, Would You Stop?".
hellogoodbye - different. Very different. Emo, kind of, but also a little bit of pop. They're the most unique thing on this list, I think.
Matchbook Romance - I'm gonna call this emo, but apparently some people disagree. I don't care. "Your Stories, My Alibis" is decent, so is "Vindicated" (which happens to be on the Spiderman 2 soundtrack)
Senses Fail - Get "Buried A Lie". If you like it, listen to other songs.
Never Heard of It - Fun, if not very unique, punk. I like Let's Go All The Way, She's A Dick, and Satisfied, from the CD 11 Days.
Unwritten Law - Punk. They recently released a video for the song "Save Me", from their new CD I believe. I don't like it that much, honestly-- however, anything from their first CD (self-titled) is a good bet.
NOFX - I own two songs; both of them came from Rock Against Bush compilations. They're pretty good, I think. I haven't heard anything other than those few, though.
Misfits - Old punk. You may or may not like them, I dunno-- and there's others here that will likely be able to recommend better than I specific songs, but try Last Caress, Helena and Die, Die My Darling.
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I could go on. Check my audioscrobbler (link in my sig), and if I decide to upload my Winamp playlist, check it too. I'll probably put it right next to the audioscrobbler link.
EDIT: I was trying to stay away from the harder stuff, but definitely everything mentioned by Rye and Exonerate.