How many dimensions are there ? 4, 11, 120

There are certainly at least four.

Other likely suspects include 10 and 26 (or is it 24? - must check those string theories)
sorry but if I knew how many dimensions there really is, I'd be god

I guess the most popular number right now is 4, but anything is possible
X, Y, Z, and some people like to consider Time a fourth dimension even though it is not akin to those three but is merely the state of things changing/moving, et cetera. (I personally think time is linear by the way). All the other dimension ideas are mathematical constucts with no basis in reality that anyone has EVER been able to demonstrate outside of flashy computer graphics and blaclboards. All physical dimensions are combinations of X, Y, and Z. The rest is people absorbing budget excesses by thinking up tricky maths stuff.

Yes, I'm a cynical bastard.