I was recently employed as a contractor. I got, and accepted, an offer for a full time position with another company (with quite nice benefits). I asked friends about whether I should give notice or just quit, they said give notice. So I did, and the next day they fired me. There was no hard feelings, I understood it didn't make sense for them to keep training someone for a job he wasn't sticking around to do. But it did put a bit of a crimp on my finances as I had some unexpected time off before starting the new job.
If I could do it again I'd wait until Friday and just quit.