There are 18 civilizations in Civ5 vanilla and 4 additional as downloadable content, each with its own leader and unique unit. In addition, every leader has a semi-unique "personality", consisting of traits that determine their in-game behavior.
For example, Elizabeth of the English, a historical naval power, emphasizes a pursuit of naval dominance and the choices she makes reflects this desire. However, in order to prevent leaders from becoming too-predictable, these traits have the potential to be changed slightly and weighted differently before a new game begins, keeping diplomacy fresh.
-Martin