Cyclops can't turn off his optic blasts. When he was young, Cyclops was thrown from a burning plane and suffered a head injury upon landing, damaging the part of his brain that would've controlled his mutant powers. (The Marvel Saga #4)
Brother's Cyclops and Havok's mutant powers are both capable of incredible destruction, but for unknown reasons, their powers can't affect each other. (X-Factor #61)
Psylocke was once Caucasian (British, actually). Her mind was transferred into the body of an Asian assassin named Revanche, whose mind was transferred into Psylocke's. Dying from the Legacy Virus, Revanche had herself killed by Matsu'o Tsurayaba. (Uncanny X-Men # 257, X-Men #22, #31)
Phoenix was not supposed to die at the conclusion of Uncanny X-Men #137. The creators originally intended only for Jean Grey to be stripped of her powers, but the powers that be felt that she deserved a harsher fate. (Phoenix: The Untold Story)
Nightcrawler was the first of the New X-Men team recruited by Professor X. He was about to be killed by a mob in his native Germany before the Prof stepped in. (Giant-Size X-Men #1)
Charles Xavier isn't in his original body. It was destroyed when a Brood Queen "hatched" from it, and alien technology put his brain into a cloned body that could walk. His new legs would later be crushed in a fight with the shadow king. (Uncanny X-Men #167, #280)