They orbit like planets if you use the Bohr model for atoms, but that kind of falls apart with things other than hydrogen-type atoms (He+1, Li+2, etc.). It's neat, I have a quantum mechanics book by Linus Pauling where he talks about such archaic things as the actual orbits of electrons. It's cute :)
Anyhow, as pengwuino says, electrons do not work with this way. In fact, when you want to look at QM, you should leave all your ideas of classical physics at the door. The name "orbital" is misleading for this reason, I suppose. They aren't "orbits" in the same manner as planets (as Neils Bohr thought). They are probability density functions describing where you are most likely to find an electron, or regions of high electron density. By definition, then, it cannot describe where the electron is 100% of the short of saying, "the electron exists somewhere in the universe." Of course, that's not very useful to most problems!