A reader asked, "How many dimensions are there?" But first, it is worth answering, "What is a dimension?"
Without defining it too rigorously, I would say a dimension is essentially a direction. If we consider a drawing on a sheet of paper, it has two dimensions. This is because there are two directions in which you can move your pencil. You can move left and right, or you can move up and down.* If you want to move your pencil from point A to point B, you have move left/right a certain distance, and then move up/down a certain distance. That is, it takes two numbers to specify the coordinates of any point. Two numbers, two dimensions.
*We don't count "up" and "down" as distinct dimensions, because if you move up by a negative distance, it's just as if you had moved down.
Of course, our universe is not a mere drawing on a piece of paper. In our universe, we have three dimensions. You need three numbers to specify the location of any object. Since we're all Earth-dwellers here, the most convenient set of numbers to use are called latitude, longitude, and altitude. That is, the directions are north/south, east/west, and up/down.
But I omitted a fourth dimension: time. I think you'll agree that time is rather different than the other three dimensions. But it is a dimension nonetheless. You may argue that it is impossible to move backwards in time, but that is not important. What's important is that if we compare event A and event B, we need three numbers to specify the relative location, and one number to specify how much later/earlier event B is. The difference between time and space is a big one (don't let any amount of physics talk convince you otherwise). For instance, it is easy to get the directions north, south, east, and west all confused, because there's hardly any difference when you rotate yourself around. But no matter what you do, you will never confuse time and space with each other. (That said, there is a bit of space-time "rotation" that occurs when you approach the speed of light.)
Therefore, four dimensions is my final answer.
Wait, you wanted to hear about String Theory? Okay. It used to be that various versions of String Theory posited that the universe has 10 dimensions, or 26 dimensions. But in the 1990s, the science progressed, and the current most accepted version, called M-theory, now posits that the universe has 11 dimensions. This often prompts questions like, "WTF are those physicists thinking?" If I understand correctly, they are thinking that String theory is the most promising way to solve the problem of quantum gravity, because it naturally predicts the existence of a spin-two boson which behaves like the graviton. But that answer's much too arcane for my purposes here, so don't worry about it.
But it is a good question to ask, "How could the universe possibly have 11 dimensions when we so clearly see 4?" It is not merely a philosophical question. There are some things in physics that absolutely rely on having only three space dimensions. In particular, there is the so-called inverse-square law. If you have a light bulb in the middle of the room, then its light spreads out in all directions. The further you are away from the light bulb, the more the light spreads out before it gets to you. Similarly, the further away you are from the Earth, the more its gravity spreads out. The more spread out it is, the weaker its strength. More precisely, the strength of gravity is proportional to the inverse-square of distance. This is directly related to the fact that we have three dimensions of space. For instance, if we had four dimensions of space, we would instead have the "inverse-cube" law. It's not just humans who can't access the extra dimensions implied by String theory--it seems that gravity and light can't access them either!
This post got split into two. See part two: Dimensions in String Theory