What makes an interesting background?

For me part of the fun of portrait photography is finding interesting backgrounds. Sometimes the least expected places are the best. It could be a brick wall, a garage door or a stairwell.
I usually look for colours and textures, as well as interesting lines. When I shoot, I make sure I shoot wide open; I usually drop the f stop to 2 on my AF-Nikkor 50mm 1:1.4D. Why not down to f/1.4? A while ago I learnt, that the biggest aparture isn't unfortunately the sharpest. f/2 gives a nice shallow depth of field and works well to isolate the subject.

Here are pictures from a simple photo session with Monika. The background used...my garden.
(Click on the image to enlarge)