Parthenocissus quinqefolia or tricuspidata (Virginia creeper and Boston ivy) both develop great fall color and will cling to walls. Climbing hydrangea will need help adhering initially but produces lots of flowers. Crimson glory vine (Vitis coignetiae), an ornamental grape vine, has stunning fall color but will need some sort of support system.

Seems like one gets fall color or flowers but not necessarily both ;-)

Those first two look great for climbing and color. The climbing hydrangea is nice, but it sure is bushy. That would invite a lot of wildlife to inhabit the space, and with squirrels, 'munks, snakes and every other creepy-crawly in the area I'm sure more than one would use it as a hangout and an invitation to test nearby windows.

I'm definitely looking for something that needs little/no assistance to climb on its own. Otherwise I could just use a Clematis, Wisteria, Jasmine or something like that. They look great, but need a lot of support.

I remember seeing a climbing vine in the UK that had small white flowers, unfortunately I don't know if it had fall color, or even what it was.

Thanks for the mentions, I completely forgot about Virginia Creeper.