I always fix my own flats. I would actually feel silly taking my bike to a shop for them to fix it.
I also try to do all my own bike maintenance too. The only times I had to take my bike in was to get some work done on my bottom bracket, because I did not have the proper tool for the job. I love learning how to fix things so, if I do take my bike in, I'm always asking if I can watch to see how they do it.