It's more a question of what doesn't.....not much :-) Climbing roses (not technically a vine), honeysuckle, wisteria, clematis, trumpet creeper and jasmine are all common perennial vines available at most retail nurseries. A fair amount of shade tolerant vines available as well.

Honeysuckle foliage dies back for me most winters although plant doesn't die but looks pretty ugly with no leaves on it with so many bare vines

I have tried to grow Star Jasmine and some winters it dies completely, all plants, in more mild winters some of them survive. This winter was one of the best for Star Jasmine for me due to how mild it was.

I have had best luck with Carolina Yellow Jasmine surviving the winters.

I've had a passion fruit vine in my back yard for years and it seems to do well. It has the most amazing, unique pretty flowers! Though, no fruit yet. And it out-competes the invasive vines growing near it (morning glory and that stupid asian vine stuff). Of course, passion fruit isn't native if you're looking for that.

Passion fruit (maypop) does well in Portland. A lot of fruit drops in autumn.

Honeysuckles tried here in SE Portland have been aphid magnets, but they do draw in the hummingbirds.

Trumpet flower vines get very large.

Clematis!