I'm just going to assume that everyone knows what I'm talking about when I say "mutant powers". Let's face it - if you aren't already familiar with the term, this post won't interest you anyway.
These powers are supposed to be the product of random mutations. Most mutants are only gifted with a single power, though sometimes you'll see someone with a spectrum of powers (different sort of psionics, for example), or just a collection of unrelated mutations (Nightcrawler, for example, can both teleport and cling to walls). Strangely, though, the powers are nearly always useful - or at least, they were back when I was reading the comics.
So you have, for example, Kitty Pryde, who can phase through solid objects; Professor Xavier, who can read and control minds; Wolverine, whose healing ability accounts for his enhanced senses; Marrow, whose bones constantly grow and extend (and regenerate), allowing her to use them as tools and weapons; Caliban, who can detect other mutants; and Rogue, whose original power (to steal other people's energy and powers) left her unable to safely touch anyone.
Admittedly, some of those powers are pretty unpleasant; the idea that a mutant ability could be a curse instead of a blessing is not new to the world of comics. What you don't see, and what I would expect if capital-M Mutations were truly random, is a fascinating array of essentially useless powers.
The power to shot beams of force from your eyes is fairly impressive (even if you have to wear a dorky-looking visor to keep from blasting your friends). But what about the guy who can summon jelly from thin air? There are benefits to breathing underwater, but what about the girl who can breathe in tea? Or the librarian who's an uncontrolled projective empath: she makes everybody within thirty feet feel really happy, all the time. What would you do if you had the power to cause or cure acne? I mean, there's probably a market for that, but still... Or the power to remove impurities from the air? And what do you do with the kid whose power kills everyone who comes within sixty feet of him?
Physical mutations would be even stranger: picture the slightly pudgy fourty-something investment banker who happens to have scales instead of hair. Or the kid whose skin excretes 4-5 gallons of laboratory-pure water each day. Or the woman whose arms and legs are tentacles. Or the guy whose skin is green, because his body has the ability to use photosynthesis.
Some mutations would be actively harmful: the ability to breathe methane might be cool, but not if it means you can't breathe air. The Blob's ability to fix himself in place is great, but only because he can turn it off. Let's face it: in a world like the Marvel Universe, where sudden and radical mutations are causing huge changes in the human species, we should also be seeing an alarming increase in stillbirths. There should be horror stories in every newspaper about children who hit puberty, manifested a mutant "power", and died on the spot: summoned fire and died from smoke inhalation; found they could fly at supersonic speeds, and died when they tried to land; tried to change shape and couldn't maintain basic biological processes; or, with the methane-breather above, died on the way to the hospital because nobody could figure out how to save her in time. Some would probably explode, for one reason or another, possibly taking out other people or even whole continents.
A world with mutant powers should have a whole lot more random weirdeness than I've ever seen in comics.
UPDATED: My brother reminded me about this video...
(caution: includes violence)