There are as many types of wizards as there are fantasy universes, at least in theory. In practice, most tend to fall into one of a few distinct archetypes:
1- The traditional. Beard. Pointy hat. Staff. Immense power in theory, but in general tends not to do too much on screen, on the basis that it unbalances the story.
2- The natural. Most wizards pore over dusty tomes, but this one has an inborn talent instead. Glosses over that whole knowledge is power angle, but raises some interesting nature v nurture questions.
3- The puppet of things beyond. Power from sources that probably want repaying at some serious interest rates. Tends to be distinctly unpleasant, but can be fun when you want to lend some edge to a good character.
4- The schemer. Wizards are clever. Because they are clever, they hardly ever bother with trying to use magic to do things directly. Instead, this one sits in the shadows, manipulating people for good or bad.
5- The mad scientist. Sometimes, magic in fantasy is just knowing one or two extra facts about science. Usually by doing dangerous experiments to find them out.
So what about your fantasy? What sort of wizards do you use? Do you use them at all?