Second: Suffering for it. Look at Gaara. Before beaten by Naruto, he was hated by everyone. But look how strong he is!
If your character has ability that was not/cannot be obtained by training, the character will probably have to suffer. Have them picked on as a little kid because they’re different. While in any character it might create a drive to be superior, anger, hatred, etc, in an overpowered character it creates balance. Someone who was a freak from birth will be treated like one all their life, even if they do save the world, by at least by a group of people who cannot change, if not everyone else as well. Ostracism, witch hunts, rejection, broken hearts, mental or social problems, physical distortions…while this does not provide the reason for their power, it certainly projects the feeling that it’s not all sunshine and daisies.
The third way is to bargain for it. Sasuke offered his service to Orochimaru for several years, and in return the curse mark makes him stronger.
This basically means they bought their power, either with their capital (Sword of Smiting for 20 gold coins!) or with their deeds (slay the dragon and I shall give you the Sword of Smiting!) This is the best means to explain ownership of powerful items, political power or extremely great education.
There are a few other reasons a character may be powerful, but they can probably be assigned to one of the categories. Just make sure that the power was earned, and any human will tell you it’s not a total Mary Sue. If that fails, just give’er a massive weakness.
