A little typology of wizards (alternatively sorcerers, magicians) in classic fantasy literature:
The Mentor/The Guide. Aka the Gandalf. Elderly, grumpy (and/or violent and/or creepy and/or other character flaw), powerful, but tends to be incapacitated at one point or to become the Good Ghost. Grandpa figure.
The Evil Sorcerer. A very wide and complex category containing many subtypes: the Transcended-into-Monster, the Traitor-to-the-Good-Guys, the Majestic Evil Lord, the Petty-and-Nasty-Underling/Sidekick...
The Promising Young Thing: the young wizard or apprentice sorcerer destined to become the greatest archmage there ever was. By the examples of Ged and Puck, used to suffer a tad bit more than what the modern "Harry Potter" influence makes believe.
The Funny Wizard: A category as large as the Evil Sorcerer and with its own sub-types: the Untalented Wizard, the Scholar Parody, the Mess...
The Byronic and gloomy Anti-Hero, who tends to bring his own doom upon himself. The prettiest "ugly" person you ever met.
The Gay Martyr. Always tragic, always queer. Made to sensibilize people to the hardships of queer people. So it means they'll always be a pretty youth who will be tortured by the universe.
The Excentric. Fully ambivalent in its strangeness. Can be as goofy as vile, as helpful as antagonistic, sometimes the two at once.
The Alien Wizard. That's not a human but it is pretending to.
The Goblin. The Little Shit that's on Our Side but just wants to Mess with Everybody. Specific sub-type of the Excentric, codified by the Black Company.
(And if you accept some less "conventional" fantasies you can include the Flamboyant Dandy)