Mostly. If they're wide and long enough, they'll provide good coverage. Deeper puddles or holes will sometimes let water and mud splash up beyond the coverage of the fender, though. On road bikes, I seem to get water dripping from the rear edge and then blown by the wind, but it doesn't get on my shoes. The rear always seems to work fine. On mountain bikes, I just put them on to keep mud out of my eyes and usually run without a rear fender, just the front.

You'll still get damp and have a little mud spatter unless you get the giant oversized cruiser-bike type fenders. Water always gets on you somehow. Fenders just make it more comfortable and less dangerous.