15. Aberforth Dumbledore
Albus Dumbledore's brother may well be the most low-key powerful wizard in the entire wizarding world, and that's probably exactly as he would prefer it, given his tragic past. And while he's somewhat relegated to a comedic footnote in Harry Potter history (thanks to those jokes about his supposedly "unhealthy" fondness for goats), he is only a magical outcast by choice.
Don't forget, Aberforth was able to hold his own in a three-way duel with two of the most powerful wizards who ever lived when Gellert Grindelwald attempted to use a Killing Curse on him and his brother stepped in. Ultimately, that duel caused the death of Arianna, but what seems to go largely unmentioned is the fact that Aberforth - a wizard who apparently could not even read - was able to defend against a Cruciatus Curse thrown by Grindelwald and to fight to a stalemate with him and Albus.
During the Battle Of Hogwarts he also casually stunned Rookwood, almost in passing, despite him being one of Voldemort's most gifted followers. And that's not to mention that sordid business with the "inappropriate" charms on a goat he was prosecuted for around 1982. That would be no mere conjuror's parlour trick...