Featured in comedies like "Ranma 1/2" and "DNA2," shape shifting appears to be a useful ability that can disguise a person. In both of these series, men can turn into women. In "DNA2," this is only a short-term plot device, but in "Ranma 1/2," a boy turns into a girl, a man turns into a panda and a girl turns into a cat---to name a few examples. However, the consequences of turning into someone---or something---usually involve men falling in love with men disguised as women and people adopting "pets" that are really human.
The series "Kara no Kyokai" and "Tsukihime" feature characters with a power best described as "death perception." They have the ability to see literal "lines" of death connecting the living to their moment of death. They can manipulate the lines of death to kill the living, but more gravely, they can abuse their powers to upset the balance of life and death for all creatures. At its worst, misuse of death perception powers can destroy the world by breaking the world's rules.
"Code Geass," a series in which three great empires rule the world, is one example of an anime in which a character possesses mind control. Lelouch, the son of one of the world's rulers, isn't near the top of the line of royal succession. When Lelouch meets C.C., an immortal witch, he receives the power of mind control. If he has eye contact with an individual, he can command him to do his will. With this power, Lelouch becomes one of the most fearsome people in the world. However, because of this power, Lelouch must fight against one of his best friends.
The star of "Gakuen Alice," Mikan, lives in a world in which a select group of humans naturally born with special powers attend a school for the superpowered. Mikan doesn't appear to have any powers at first, but the school's teachers soon discover she has the power of "nullification"---i.e., she can temporarily remove other people's powers at will. Mikan's nullification powers seem innocent enough, but they're rare and useful in the right context; she can turn the tide of any superpower battle. Mikan's nullification powers make her the kidnapping target of a secret rebellion group.