They are fungus gnats. They lay eggs in the soil, and the larvae eat the decaying material, as well as root hairs of the plant. We have had them for almost a year now, and they are miserable things. They’ll get right in your face. I guess they like the smell of the breath?
For starters you can reduce their numbers by not watering as often, letting the soil dry out between uses. Diatomaceous earth works, but it’s messy and unattractive. I have controlled them, but not eliminated them using mosquito dunks. Mosquito dunks are available in most garden centers, and have a bacteria that kills mosquitoes. It also kills fungus gnats. To do this I break a mosquito dunk in half and put it in a gallon jug of water. I keep the water out of the sun to help keep the microbes it releases alive longer.
Knock out Gnats was developed because the fungus gnats began to develop a resistance to the mosquito dunks.. You can buy knock out gnats on the internet, which is supposed to work better than the mosquito dunks.
Your last option is to use shiny white cards that are coated with glue. When the gnats alight on them, they get stuck. Many greenhouses use these because they are simple, effective, and cheap.
I suggest a combination of these. Here are a few links.
Knock out gnats: http://www.gardensalive.com/article.asp?ai=614
Mosquito Dunks http://www.planetnatural.com/site/mosquito-dunks.html