Paths on a grid

Consider an $n \times n$ grid. (A 4 $\times$ 4 grid is shown below)

How many paths are there from the top left corner to the bottom right corner?

(Recall that a path in a graph is a sequence of distinct vertices in the graph such that consecutive pairs of vertices are connected by edges from the graph.)

Note: There is no restriction about only moving right or down. You can move in any direction.