Punk: The Clash, The Sex Pistols, Joe Strummer and the Mescaleros, The Undertones, The Offspring, Green Day, Flogging Molly, Dropkick Murphys, NoFX (I don't really like them, but everyone else seems to), Leftover Crack, Millencolin, Goldfinger.
Ska: Voodoo Glow Skulls, The Mighty Mighty Bosstones (ska-core), Rancid, Less Than Jake, Mad Caddies, Choking Victim, Catch 22 (only "Keasby Nights" album), Streetlight Manifesto, Rx Bandits, Reel Big Fish, The Pietasters, Suicide Machines, Sublime.
That should cover it for now. The ones that I highly recommend are Sublime, Mighty Mighty Bosstones, Mad Caddies, Reel Big Fish, Flogging Molly, Dropkick Murphys, Catch 22 and Streetlight Manifesto (practically the same band), The Offspring, and especially Rancid, who are the closest thing you'll find to Operation Ivy (while still keeping their own style).
EDIT: Reel Big Fish is neither punk nor ska-core. And if you want some ska recommendations, I'm a ska geek

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Quote of the week:
"I went to a fight the other night and a hockey game broke out."- Rodney Dangerfield.

Pointless fact of the week:
The word “trivia” comes from the Latin "tri-" + "via", which means three streets. This is because in ancient times, at an intersection of three streets in Rome, they would have a type of kiosk where ancillary information was listed. You might be interested in it, you might not, so they were bits of “trivia."
[ June 08, 2004, 12:10 PM: Message edited by: Just across from Wayne's Junk Store ]