DNA.
Just about every mainstream science fiction film/tv show/whatever I can think of from recent years uses altered DNA to explain superpowers, whether it's through laziness or obsessiveness, writers nowadays seem incapable of original explanations.
The fantastic four had their DNA altered by cosmic rays, the characters in Heroes have mutated DNA, in the new Hulk film the hulk inherited modified DNA from his father.
It was fine to do this years ago, but now it's a cliché which has gone far beyond the end of it's life [/rant]
Actually, how else would give a character super-powers? It's actually very limited.
-Power through SCIENCE aka science is evil but not if you happen to be American:
a.) Either cosmic rays, ominous particles or other weird phenomena. Mostly due to accidents. Lightning is just fine.
b.) Technological enhancement. If it happens to be artificial limbs expect lots of fauxlosophical rambling about "loss of humanity".
c.) DNA manipulation, super serums and other artificial stimulations. "What man was never meant to be/see/do" - expect to die a horrible death.
-Power through MAGIC aka "How it works, you ask? Just fine."
a.) The power is granted by a higher being. Alien, god or other magical beings like fairies, dragons or witches. Mostly the hero is in debt of said being or has been chosen to fight monsters of the week.
b.) It's in the blood. The hero has actually never been (fully) human to begin with and kicks ass just because of his awesome heritage. Expect such characters to be at least a bit arrogant and in the worst case to be outright racist.
c.) The protagonist finds a mystic artifact that does awesome stuff. Related to a.).
-Power through TRAINING aka "You can achieve everything if you just believe hard enough. Including magic."
a.) Training from hell. The character has to do sheer impossible tasks that he or she mostly just survives because the plot says so. Expect training montages. This goes through all genres, from martial arts and science over to the arcane arts.
b.) Survival. Related to a.), the protagonist goes through training from hell but forced from the outside and never had a choice to just live a normal life. Expect lots of angst.
Also, remember kids: ambition is evil and being dumb is good!