The electrons in an atom are not subject to the same macro-scale physics that bodies such as planets are. You start to get into Quantum Mechanics when you get to sub-atom small.
The electrons have no defined speed of rotation, though it is proportional to the temperature. An atom at absolute zero would have stationary electrons.
If you believe in Heat Death of the Universe [1], then yes, eventually the electrons would stop moving as would everything.
EDIT – Forgot to say, you can’t measure the velocity of the electrons without interfering with them Schrödinger’s cat and all that.
[1] – http://en.wikipedia.org/wiki/Heat_death_of_the_universe