I feel like we've moved past punk (or we're into "post-punk") almost as soon as punk began. There are several New Wave songs on this list ... even Prince's song is New Wavish. And the post-punk tunes. Only the Funky 4 + 1 hints at the coming hip hop onslaught. And the only real punk tune here comes from Flipper.
Joy Division, "Love Will Tear Us Apart". I've always preferred New Order to Joy Division, but this song is unstoppable.
Bob Marley and The Wailers, "Redemption Song". Covered by seemingly everyone (I'm partial to Joe Strummer's version).
Blondie, "Call Me". I tend to forget this was from American Gigolo ... just feels like one of a succession of great Blondie singles at the time.
Talking Heads, "Once in a Lifetime". A memorable video, but watching it, you might think Talking Heads consisted solely of David Byrne. I kinda prefer the Stop Making Sense version, which focuses on Byrne, but at least lets us know there are other people in the band.
The Pretenders, "Precious". The first track from their first album. As a statement of purposes, it's hard to top Chrissie's "Fuck Off!". All these years later, it's hard to explain how powerful those two words were at the time.
Prince, "When You Were Mine". As usual, it's hard to find Prince videos online, so here's Bob Mould, a contemporary of Minneapolis Prince, playing the song at the famous First Avenue just after Prince died.
The Fall, "Totally Wired". Mark E. Smith died a couple of months ago, which forced me to realize I don't know any Fall songs. Until I put this list together, and remembered I do know this one.
The English Beat, "Mirror in the Bathroom". Their first album was like a greatest hits album.
Funky 4 + 1, "That's the Joint". The infallible Wikipedia tells us, "They were the first hip hop group to receive a recording deal, and the first to perform live on national television. The group was also notable for being the first to have a female MC." Christgau named this the best single of the 80s.
Flipper, "Ha Ha Ha". I have so many Flipper stories. I've told most of them before. I called this a "real punk tune" above, but it's probably post-punk too. Sigh.