Physical
Physical powers make up the majority of mutant powers in the comics. These powers augment physical strength, inflict physical damage or give a physical advantage in a fight. For example, the X-Men's Cyclops is primarily a physical mutant who can shoot damaging beams from his eyes. Gambit can make anything he touches explode at will -- his item of choice being playing cards. Juggernaut, an antagonist to the X-Men, is physically invulnerable to almost any attack, in addition to having extreme physical strength.
Psychic
Psychic powers primarily inflict mental damage to an opponent. Professor X, the leader of the X-Men, is renowned for his psychic ability. Despite being immobile, he can use his psychic powers to attack a mind and bring it into submission, communicate telepathically with entire teams of mutants and read minds from a remote distance. These powers may also have physical applications as well; Psylocke can make psychic, ethereal swords from her arm, which attacks an enemy's mind.
Utility
Utility powers are noncombative or noninvasive within themselves, but a mutant can use them in battle if necessary. These powers typically manipulate matter and break the laws of physics and nature. Flight is a utility power. Some mutants have greater utility powers, which are responsible for a set of subpowers; for example, Magneto's magnetic powers grant him multiple abilities based on magnetism. He can fly, create electromagnetic shields, discharge blasts based on hypermagnetic forces and create matter by using magnetism in a subatomic level.
Transformation
Transformation powers typically augment a mutant who would otherwise be fairly normal. These powers are either controlled or involuntary. For example, Colossus can change his skin completely to metal at will, granting him physical strength and defense. On the other hand, while the Beast has animal-like traits such as protruding claws and reflexes, he is permanently in his transformed state under normal conditions.