My current most favorite climbing vine is Creeping Fig Vine. We have it planted on a wall in our courtyard, and it has almost completely covered the wall this summer.
Creeping Fig Vine is a perfect choice if you need to cover a blank brick or stucco wall (it will ruin wood). Its dark green heart-shaped leaves can transform a blank wall into a lush, green screen, and it can be shaped into a design, or just left to randomly cover.
This is a picture I found in Southern Living, which shows how it can be trimmed to grace a blank wall and steps at an entrance (I love the idea of wrapping the steps!). The article said that one quart-size plant is responsible for that beautiful entrance.
Fig Vine is very easy to grow and can handle a vast range of light conditions, from mostly shade to full sun. It requires no fertilizer in most any soil conditions, and has no serious pests or diseases known. The only down side is that it is a somewhat high maintenance plant, because it is capable of covering everything in sight if not kept under control.
Size: Capable of eventually covering a three- or four-story building