Lots and lots of clematis!

Climbing hydrangea for more shady locations.

Honeysuckle - check with someone local for which ones will do best for you.

Climbing roses - with the caveats that it needs to be disease resistant, and grown on something with easy access for maintenance, especially if it's a vigorous rose. I came to the conclusion that the best way to grow them is on something like a rail fence or swag chains or rope, as long as it is located where you have easy access from both sides for pruning. Most climbing roses flower best on new growth on horizontal canes. The easiest way to get that is to grow them across something, rather than the usual way of growing them up an arbour.

I have not been very sucessful with Schizophragma hydrangoides or kiwi vines, but that's because I don't have the right spot for them I think. Wisteria is lovely (mine started flowering yesterday) but I would not grow it as a vine, only as a tree.

Thanks woodyoak! I have written them on my notes. :)

My list is similar to Woodyoak's:

Honeysuckle - look for varieties of Lonicera sempervirens, a native red-flowered honeysuckle (though also a few yellow or orange types), that grows well around here and attracts hummingbirds. Try to get a variety that says it is mildew resistant if that is likely to be a problem for you. Mine isn't a named variety, but I have never had mildew problems.

Clematis - My favorites! I especially like the summer flowering, hard prune varieties or the really early flowering atragenes (no pruning) as they aren't likely to wilt and bloom at times other than my main flushes of perennials.

Hydrangea anomala subspecies petiolaris and Schizophragma hydrangoides are both shade-loving extremely large vines with hydrangea-type flowers. I have a plain green Hydrangea anomala subsp. petiolaris growing up a large retaining wall, but it also grows well up tree trunks. There are also some varieties with variegation on the leaves, like Moonlight and Miranda, but regardless, be sure you have room for this one if you are going to plant it.

I do have some of the hardier climbing roses, but for me they have to be single early bloomers or they need attention to removing Japanese beetles daily.

I am currently trying a hardy kiwi for the first time. One of my across-town neighbors grows it, so I am hoping that our conditions are similar enough that I can be successful. The fruit of hers is delicious. I honestly wouldn't call it a beautiful vine, however!

If I were going to plant wisteria, I would be more likely to use the American wisteria as it isn't so rampant and invasive, though it still is a large vine needing attention to pruning. Both the Chinese and Japanese tend to seed around and need much management as far as pruning, way more than I have time for. There are horror stories out there of sprouts from roots meters away from the original plant.

In all honesty, there are a couple of annual vines I really like as well:
Sweet peas (for sentimental reasons since my grandmother grew them) have lovely scented flowers. I would NOT recommend perennial sweet peas - no scent and they seed around horribly.

Scarlet runner beans have bright red flowers that attract hummingbirds, and as a bonus have edible beans, either very young as green beans or dried beans with a lovely purple mottled color.

I also like black-eyed Susan vine, Thunbergia alata, with its cheerful yellow or orange (or more rarely white or pink) flowers with dark eyes.