Akebia quinata, Hydrangea anomala, Jasmine nudiflorum, Actinidia kolomikta, Passiflora cerulea, Schizophragma integrifolia, Pilostegia viburnoides, Clematis, the list goes on - some of these are evergreen, some aren't, some are twiners, meaning they need something twine around, some are self clinging

If you look at the GoYpedia page on "climbers" and "evergreen climbers" you might find some inspiration there...