Nightcrawler's main power is that of teleportation. He can move himself and what he's carrying to nearly any location that he has seen. The farther he tries to teleport though, the more the risk he has of teleporting into a solid object. Nightcrawler teleports through an unknown dimension and leaves behind the smell of brimstone. This ability allows Nightcrawler to teleport in and out to attack his foes or make a speedy retreat.
Kurt is also extremely agile and is a trained acrobat and gymnast. He has a prehensile tail that is extremely strong as it can lift a human being and support Nightcrawler's weight in his acrobatics. His feet also have a prehensile quality which he can use to hold himself up and cling to walls.
Nightcrawler's blue fur allows him to blend into the shadows. This ability has also been tied to the dimension he travels to when he teleports. He can even appear to be in the shadows in broad daylight.