The X-Men's Bishop has the weirdest secret power. In the early 2000s, Marvel's X-Men comics hit upon the idea of secondary mutations. These allowed previously established superheroes to develop new powers that had never been seen before. In some cases they were quite cool - Emma Frost gained the appropriate ability to shift into a diamond form - but in others, they were frankly bizarre.
Take the example of Bishop. A time-traveling mutant from a dystopian future timeline, Bishop's traditional power is the ability to absorb and project energy in almost all its forms. It's actually a passive ability, meaning he's always absorbing energy in its various forms around him; even the friction generated as his body moves through the air charges him up. Exposed him to lightning, magnetic fields, or anything of that kind, and he basically becomes supercharged. But in the early 2000s, Bishop gained a new power.
In Uncanny X-Men #452, Bishop revealed he's basically a mutant homing pigeon, with an innate sense of where and when he is at all times. No doubt this is quite convenient for a time traveler, who has frequently found himself bouncing around the timeline. In this case, though, it was demonstrated in a rather amusing way; the X-Men had been unexpectedly teleported across the world and appeared in a random sewer. Bishop immediately knew where he as. "We're in Paris," he told the rest of the X-Men as he scrambled to his feet in sewage water. "Cinquieme Arrondissement, near the Rue Dante. What can I say? My body instinctively knows where I am. I can't get lost."
This was during Chris Claremont's return to the X-Men comics, and he rather seemed to like giving Bishop additional powers for pure convenience. Bishop's new ability essentially served the purpose of accelerating the plot, because the X-Men could know exactly where they were without having to go to all the trouble of figuring it out. Later in the same arc, Claremont also gave Bishop a convenient immunity to nanotech, for similarly convenient plot purposes.
Oddly enough, Bishop's weird "homing pigeon" power is actually quite appropriate for his new role in Jonathan Hickman's X-Men relaunch. He's now the Red Bishop of the Hellfire Corporation, responsible for distributing mutant drugs across the world, which means he's one of the mutants who spends the most time off of the living island of Krakoa. An instinctive sense of where he is at all times will be highly useful - if seriously random.