Nikola Tesla/WMG

Tesla told nothing but the sober truth.
He did cause the Tunguska Event. And he did speak with Martians. And he did build a 1920s-style Death Ray.
 * The business with the pigeons was a total fabrication, however.
 * We can lay to rest all the ones about the trouser button.

Tesla's Death-Ray was stolen by the Russians and made into a planetary laser cannon which protects us from aliens.
Or so some crazy conspiracy nuts believe, based on grainy artifacts in some old orbital footage which seems to show a line of something coming up from Russia and scaring away something floating up there.
 * On the other hand, his death ray requires an atmosphere, or some other physical medium, based on what are by far the most probable designs for it. Good luck hitting an alien spaceship with a weapon that doesn't function in space.
 * Well, duh, it's pretty obvious, innit? Space has an atmosphere.

Tesla is another Goblin King.
Think of it. Advanced technology, frequent misunderstandings from mortal points of view, childlike delight in making complicated death traps for ultimately mutually advantageous ends... remind you of anyone? He's simply the good (and thus brunette and mustached) twin to Jareth the Goblin King. This also explains why David Bowie looks so much like him. Eccentric, intelligent, oddly attractive to modern mortal women despite his sheer peculiarity... oh, to hell with it. He's ALSO Jonathan Crane from Batman Begins.
 * This troper certainly loves whoever wrote this.
 * Does this mean Tesla had a super-powered crotch as well?
 * Or rather, Tesla is Crane's father and The Prestige takes place in the same universe as Batman Begins.

Tesla is David Bowie's father.
And thus the Goblin King lineage is safely passed down.

Nikola Tesla is Santa Claus.
VTOL aircraft. Matter duplicator. Reclusive eccentric. Saint Nick.
 * Looking at Santa's page, this makes Tesla The Doctor and Stephen Colbert, too.

Nikola Tesla was a vampire.
He infected a British doctor from the 19th century with a special strain of his vampirism, making her immortal. She would later join the Stargate program.
 * Jack the Ripper, the Invisible Man and Sherlock Holmes were also infused with vampiric blood.
 * Don't forget the 1944 vampire movie, Return of the Vampire. The vampire was an evil dark scorcerer. His name:Armand TESLA

Tesla designed a matter resonance device far more effective than his original and destroyed everything.
Quantum physics is a result of everything having been shaken apart at the subatomic level. The reason things at that level don't follow Newtonian physics is that each particle is free-floating and moving around and through everything next to it at a rate of less than a planck time unit. (This should be impossible, but hey, it's Tesla's invention. They're not shown to follow the laws guidelines of possibility.)

== Tesla and Edison invented the War of Currents as a joke, never became enemies, fought eldritch abominations together with steam-punk technology, faked their deaths, raised a young man to continue their legacies in a city-sized ship that can go between universes, and died fighting H.G Wells's Martians. == ...What? Please tell me this movie is coming out next summer...
 * Tesla is M's boss.

Tesla is a Spark transplanted into this world by an experiment gone awry
Thinks about it! Feats that modern science has yet to recreate. Uncanny insight. And, as the jaegers would put it, frequently 'in the madness place'.
 * Alternativly, this world also had Sparks, only instead of the veritable hoard of them that exist in Girl Genius, we only got a few, withh Tesla being possibly the Spark-iest of them all.
 * ...Or an experiment Gone Horribly Right.
 * Genius: The Transgression suggested that Tesla was an Etherite.

Thomas Edison created Science-Related Memetic Disorder to discredit Tesla
Let's look at the facts:
 * Edison's characterization of Tesla inspired a lot of B-movies featuring Mad Scientists, helping establish the trope.
 * Tropes are a type of meme.
 * Memes have a tendency to mutate out of their creator's control.
 * SRMD is a memetic virus that causes its hosts to act out the trope.

Tesla is Kamina.
Think about it: We never know what the afterlife is like, if we reincarnate, and where we were before we were born. Perhaps, the TTGL Universe is the Womb World, where we stay before we're born. When we die there, we come to Earth in a random time and place. So, after Kamina died, he appeared as Nikola Tesla. Proof? His obfuscating manliness and advanced, if not crazy, ideas. He helped bring Humanity to the surface, guys. He helped people to pierce through the Heavens with his courage and intelligence.
 * . . . to which we can add an extra degree of inspiration by noting that Tesla was sickly in his youth. So, not only did he become the King of GAR, he had to overcome physical limitations to do it!
 * Sickly? So, he wasn't Kamina, but Captain Ukitake!

Tesla is a shinigami.
He kills people with lightning, you see.

Tesla is a ghost.
He accidentally discovered a dimensional gateway, but his attempt to pass through resulted in his death on this plane of existence. The portal just happened to lead to where he was going: the Ghost Zone. He took the name Nikolai Technus so that when he met up with anyone from Earth, they would be scared sh* tless and not just think he was crazy.

Tesla is Tesla
He's a

Tesla created a Time Machine, faked his death, and traveled to the future.

 * He could never find the funding, the time, or the equipment to do what he wanted, and the world just wasn't ready for some of his ideas. This is why he invented a time machine, faked his death, and traveled to the future, where he will be better able to do what he always wanted.
 * However, due to his eccentricity, he only goes to dates that are divisible by three, such as 12/21/012. Wait, Nikola Tesla with adequate technology and funding!
 * Possibly an Oh Crap, but also possibly one of the things to ever happen EVER.

Tesla was from the future, and went back to create a Stable Time Loop
In a few centuries, Nikola Tesla will be born and, as he grows up, realize he bears more than a passing resemblance to the historical Tesla. Learning he is, in fact, the real Nikola Tesla, he will travel back in time to fulfill his destiny. He will then invent (I mean, he invented...) all the technology that will shape the future that he comes from. Knowing, of course, that too much interference with the time line will destabilize the loop, he will be perfectly content to let Thomas Edison take credit for his work, and of course he'll remain celibate to avoid any nasty in the pasty. Of course, before he leaves the future, he'll announce his intentions to the world, and will become known as a Big Damn Hero for his willingness to remain in the past, and will finally be recognized as the greatest inventor of all time.
 * And then the above theory happens, and Tesla returns to the future to find prestige, funding, equipment, and the respect of the people who's lives he helped.

Tesla was using Magic-Powered Pseudoscience.
The source of his magic? He said it himself: Virgin Power.

Tesla was a Zoophile.
Came off as asexual most of his life but had a very high "fondness" for animals and especially a bird later in life which when died was considered the end by Tesla in regards to his life work.

Tesla's head weighed, like, 20 kg.
Seriously, look at some pictures of him. 9 times out of 10 he's supporting his head on his fingers.

Tesla was not the Tesla, but a Tesla: not a human, but a transdimensional personification of harnessed electricity.
Or something like this. It is the reason why advanced electrical stuff is always Tesla-something even in fantasy worlds completely unrelated to our own.

Tesla was a Time Lord
He disguised himself as a human for some reason, Family of Blood style, and made a career as an inventor, subconsciously using his time lord knowledge to make inventions way ahead of his time.