I have a half dozen or so vines around the backyard fence. Probably the one that is easiest to maintain and trim is the white star jasmine. Covers the fence nicely and I trim it just even with the top of the fence. Blooms once a year and smells great.
Others I have are
sweet autumn clematis - deciduous, reseeds a bit too much
Yellow conderate jasmine - not as tame as the white star jasmine
Coral honeysuckle - nice
Purple hyacinth vine - annual, not tame at all
Tangerine beauty crossvine - its whole goal is to climb to the top of a tree
Cypress vine - annual, too crazy, grows only to reseed all over the yard.