There is a bunch of different punk types. There is hardcore, pop punk, old school, political, funny, punk/ska fusion, etc. It kind of depends what you're into.
Here's a few starting suggestions though. For old school kicks, start with The Ramones and The Clash. Both are staples you can't wrong with. If you'd like something more pop and funny try the Descendents or the Vandals. If you like political punk try the Dead Kennedy's. If you want some darker try the Misfits or T.S.O.L. If you want something hard try Black Flag. Try the Germs if you want some raw. Try Fugazi if you want something a little different. Go with some Operation Ivy if you might like the punk/ska mix.
There are a ton more bands for each style though. Try some compilation CDs and find what you like. Typically they're pretty cheap (like $5 or so) and can have 20-30 songs, each by a different artist.