Here's a few that might work;

http://www.thegardenhelper.com/vines.html

If it is part shade, there are several varieties of clematis that you could try. I have 'Silver Moon' growing on the north side of a slatted fence, under a Heptacodium. It gets little direct sunlight, but still blooms well. This Spring it's had 20 blooms. 'Hagley Hybrid' & 'Nelly Moser' are also recommended for partly shaded conditions.

We have two honeysuckles that do okay in part shade. For full shade climbing hydrangea is beautiful. Entling is right about some of the clematis. We have a Nelly Moser that does well in part shade.

I love my Sweet Autumn clematis that grows in about 1 hour of sunshine each day. It is a FAST grower with tons on small white flowers. Beautiful! Also Silver Lace vine, which also grows in about 1 hr sun, but can pull down a trellis if you're not careful!

Zephirine Drouhin Climbing Rose. Great for shade,,very fragrant, bright pink,,nearly thornless.