I also looked into it a couple of weeks ago, but then decided against it. The main reason for this was that my PC was not powerful enough to make it worth my while.

The mining of Bitcoins relies heavily on repetitive tasks/calculations, something GPU's are hundreds of times better at than CPU's are. And, even though I have a very recent (Ivy Bridge) Intel CPU, I also use the internal GPU of the CPU for video tasks because for my use, this GPU is more than adequate. (I don't ever game)

In other words, to do some decent Bitcoin mining, I would have to buy a new video card, which would consume A LOT more power. The investment of the video card alone immediately kills the deal. But even if I were not to consider that, there's also the fact that the video card would consume so much extra energy, my electrical bill would increase x-times more than the value of Bitcoins I could ever gain through this mining process. In other words: it's a bad deal.

Oh, and yes, as Dan says: it's not really anonymous paying, not in the way they make it seem out to be. Sure, you could use an alias. Maybe even pay while being anonimized though TOR or something, but in the end I'm pretty sure there will always be a trail.

The second reason was not all that important to me, but the first one was. At first I thought this could have been a way to make money from the unused CPU/GPU cycles of you computer, but in the end you'll more than probaby loose money, if you count all the factors of cost.