How many dimensions are there in the Universe?
Hard to say for sure. But IMHO more than three. You can tell because of gravity. It's a "force", but there's no maelstrom of whizzo magic messenger particles zigging between you and the ground making you fall down. Or making the moon go round in circles around the earth. What gravity is, is a
distortion of the three regular dimensions, in some other dimension that you don't otherwise notice. The analogy is a bowling ball weighing down a rubber sheet. If you flick a marble at it, it rolls around the depression, in an orbit like the moon's orbit round the earth. The thing is, you're part of the rubber sheet along with all your rulers and light beams, which is why you don't notice the distortion directly.
http://en.wikipedia.org/wiki/Curved_spacetime

There are of course, other forces.