I thought it was a special soft drink (Gingold?) that he noticed that all the sideshow rubber men drank.
The Black Cat (sometimes on the side of good) made a deal with the Kingpin to gain her luck powers.
IIRC, Luke Cage volunteered in prison for his experiment. And his former partner, Iron Fist, went through the trials in K’un Lun to become the Iron Fist.
That may have been his ultimate goal, but acquiring magical abilities was a deliberate choice for achieving that goal. Or at least I think so – I believe I’ve just heard about recaps of Dr. Strange’s origin rather than reading it first hand.
Also, I’d like to throw Spider-Man partially on to the list. Sure, he got most of his spider powers via accident, but he followed it up with intentionally inventing his web shooters. So one of his most iconic powers was still sought out. Of course the movie version goes with the more reasonable explanation that the webs were part of the whole spider bite package, but the original comic canon had it as an invention.
Actually, he sought out the Sorceror Supreme of Earth (under the pseudonym “The Ancient One”) to fix his nerves. The Ancient One then offered to take him on as an apprentice and he refused. But Strange was stuck in the Ancient One’s castle (in the Himalayas) by a blizzard. That night, the AO’s apprentice Baron Mordo attempted to kill him and become Sorceror Supreme of Earth in his place. Witnessing this, and being mystically bound by Mordo to keep him from warning the AO, Strange has a change of heart and decides to accept the AO’s offer.
He not only wasn’t looking for it originally, he refused it when it was offered.
Originally, Wonder Woman’s powers were a result of her Amazon training, meaning that she had to work in order to gain and maintain them. And, of course, she had to compete for the title of Wonder Woman (which is why she got her golden lasso).
When Quicksilver lost his powers as a result of M-Day, he sought out various ways of trying to get them back, finally settling on exposing himself to the Inhumans’ terrigen mists.
The Silver Surfer might sort of count, in that he volunteered for Herald duty rather than have Galactus eat his planet.
The Golden Age Starman–inventor of the gravity rod.
The Golden Age Hourman–invented Miraclo tablet, which give him superstrength, stamina & invulnerability…for one hour. Must wait another hour to take the next tablet.
Henry Pym–Ant Man/Giant Man/Goliath/Yellowjacket
Jan Van Dyne–the Wasp
I don’t quite understand why Iron Man counts, but Batman doesn’t. Their “powers” both stem from exceptional, but not superhuman, natural abilities.
Right. And he then developed a concentrated extract of the fruit that the soda was made from.
Aaaah…okay. I’d always just assumed he was drinking the soda.
Night Girl. Lydda Jath deliberately let her father use his “super-power ray” to give her super-strength, because she had a crush on Cosmic Boy and wanted to join the Legion of Super-Heroes to met him. Unfortunately, her homeworld of Kathoon is always in darkness, so the super-strength only worked in darkness. Having super-strength only half the time was not a cool enough power for the Legion.
She did marry Cosmic Boy and they had a son.
Was he successful?
Yes. Yes he was. And the second Invisible Kid was Jacques Foccant, who took the serum to stop the evil Computo, who was inhabiting the body of his sister Danielle.
No one knows. He hasn’t been seen since.
Nova volunteered to become a Herald of Galactus because she wanted the powers and to see space, not to save Earth.
Rom and his fellow Spaceknights volunteered to become cyborg warriors.
I don’t remember how Billy Batson learned the magic word to give him super-powers… whether he had to find it or whether it was sheer accident or what.
As an aside, relatively recent events have indicated he may well go back to some level of villainy (or at least antihero-ism), but with the “mega-event mania” hitting both Marvel and DC, there hasn’t been much done with it yet.
Oh, and why is this in the Game Room? 
In most versions, he stumbled upon the wizard Shazam, who told him.
I always thought he heard it while having really good sex with Jim Nabors.
I have no idea. I meant to post it in Cafe Society.