To answer the original question, I have only moved my capital once or twice in all of the games I've ever played. Under the advanced government types, there does not appear to be a genuine reason to move it.
However, I can understand Dark Ascendant's rationale for wanting to move it. Its been a long time since my capital came under attack!

I do try to build cities outward from the capital, though, because of the corruption inefficiencies in early governments. When this isn't possible due to geographic constraints, I compensate by building additional defensive units in the capital and the immediately surrounding cities. I will even tailor my military strategy to go after the AI closest to my capital.
I seem to recall that in one of my early games of Civ2, I lost Washington to the Romans

, and had serious trouble getting it back. Needless to say, I lost that game.
Generally, I have more constructive things to build than another palace, though.