Affordable starter lighting kit for portrait photography with a Nikon D80

I'm going to recommend slightly less than half of what @cmason suggested: One light, one umbrella, one light stand. See also the Strobist starving student kit. You can get an SB-600 and then have wireless control over your camera for not much more.

The reason I recommend one light over two is that it works just fine for a lot of portraiture. (Check out the excellent Q&As tagged with lighting basics; most of the techniques are based around only one light). Make no mistakes, having two (or more) lights gives you more flexibility than just one. However, you are looking to "not break the bank", and so starting out simple seems advisable. You might also want to get somewhat different components as you upgrade over time: a different make of flash, a soft box vs an umbrella, a different stand, a different triggering system, etc.

Also, I don't think a super clamp is strictly necessary. I definitely wouldn't get one instead of a light stand. Again, it's worth having once you're ready to spend more for more flexibility. (Don't forget though that you'll need an umbrella/hot shoe adapter for your light stand.)