OK, sorry to echo most of the replies in this thread, but JJ Brunell of The Stranglers and Paul Simonon of The Clash were definitely 2 of my favorites, but there were others as well.
Screamin' Sam (Sam Ferarra) of The Ugly and then The Viletones (in the second lineup of that band) was/is incredible. He made playing a Hofner violin bass look so cool! Unfortunately it's almost impossible to find any vinyl with him playing on it from this period (late `70's, early `80's) except for the 1983 live album of The Viletones, "Saturday Night Sunday Morning" (which is so rare, I would gladly pay $200 for a copy of that album)
Also, even though they were post-punk by this time, The Gun Club in their second (and most critically acclaimed) lineup, featured Patricia Morrison on bass (not the one who married Jim Morrison). Best album from this era was "The Las Vegas Story". She eventually joined The Sisters Of Mercy and finally ended up playing with the newly reformed Damned. She was eventually replaced in The Gun Club by Romi Mori (Jeffrey Lee Pierce's wife) who was an even better bass player, but, by this time The Gun Club were far too slick to be referred to as punk.
Oh, oh oh! And how in the hell could I forget Richard Hell?!?! He made playing a Mustang bass look really cool! He was the original bassist for Television, but Tom Verlaine kicked him out for constantly jumping around and upstaging him (he was trying to teach you something called showmanship, Tom), he went and formed The Heartbreakers (nothing to do with Tom Petty) along with Johnny Thunders. These guys went over to England and met up with the infamous con-artist, Malcolm McLaren, and became the first real punk band. Richard got bored and soon moved back to New York, where he formed Richard Hell And The Voidoids. Best known for the song "Blank Generation". The Stray Cats actually ripped off the bass line from this song for their first hit, "The Stray Cat Shuffle". Mike Watt claims Richard Hell as one of his early influences.
Got to admit, even though they're more pop than punk, the guy in Green Day is really f'n good.