The Dude already mentioned The Ramones, but they've got so many great covers. Besides what he mentioned check out stuff like Do You Wanna Dance?, California Sun, Take it As it Comes, and Joey Ramone's cover of The Stooges' 1969.
The Misfits doing Blue Christmas. This is a bootleg but hearing Glenn Danzig do Elvis is always a treat. The segway into We Are 138 makes it even better.
Years later Danzig would do a proper studio cover of an Elvis song. It's great.
The Descendents do a great cover of The Beach Boys' Wendy.
Since I mentioned the Descendents, their sister band ALL plays a cool version of Hot Rod Lincoln.
And then Lagwagon does a good punk version of Bad Moon Rising.
I don't really care for U2, but this cover by Ignite made me like at least one of their songs. It's really good.
Black Flag did a lot of versions of Louie Louie over the years, but this one is my favorite. Henry improvs more on this than on any other version of it, and it's great.
Finally, (almost) anything by Me First and the Gimme Gimmes. The Gimmes are a punk rock supergroup and professional cover band. They cover all sorts of songs in punk form, often mashing up other parts of old punk songs in with the old classic song they're doing. This cover of My Heart Will Go On is different in style and closer to celtic punk, but this version of Karma Chameleon is more like their usual work: