Actually, I should have said 'infinite density'. A singularity, at least according to the equations of general relativity, has infinite density but finite mass (the mass of the star that collapse minus what blew away). But anyway, 'infinite density' is just a physicist's way of saying we don't have a clue. Infinity is generally not a good thing.
If you did travel at the speed of light you'd have infinite mass though. Which is why you can't.