There have been many debates and answers when trying to find out. From this, I have always wondered if, without evil powers, could the Avatar be evil? Not like an anti-avatar, but the main, chosen avatar themselves be personally evil? For this term of "evil", I mean as in they are not anti-heroes or misguided good guys. What I mean is if the avatar becomes greedy and a celebrity, and then forms a god complex and so on. From things like this, or even something like antisocial personality disorder, could the Avatar become evil, like say, where he/she is their world's equivalent to Homelander?
In a word, no. Since the Avatar (capital A) is an avatar of the Spirit of Light, Raava (combined with the body and spirit of whoever is chosen as the reincarnation of Wan), it's simply not possible for the Avatar to be evil, any more than light can be dark. I think we can assume that if the host wasn't pure of heart to begin with, they couldn't be the avatar of the Light Spirit. The very idea would be a logical contradiction.
That all being said, not all avatars (small a) are good. We encounter the Dark Avatar (a fusion of the Spirit of Darkness, Vaatu with a human named Unalaq) in the episode AtLA: Darkness Falls. They're very very naughty indeed, with their stated aim being to usher in "a thousand years of darkness"