1. Doctor Doom, The Murderous President of 2099
Writer Christopher Priest's stellar, late-90s run on Black Panther mostly concerned itself with redefining its title character. At the same time, however, it established an upper-crust of heroes and villains. Super-beings whose primary roles went above and beyond hero-on-villain brawls, and instead focused on the power, privilege, and burden of rule. Three guesses as to whether the sovereign of Latveria made the cut -- alongside the Panther himself, then full-time villain Magneto, and ever the moral flip-flopper Namor.
Doctor Doom was born to rule. Not even waking up in Marvel's bizarre cyberpunk dystopia known as the 2099 Universe could shake that out of him. Though when he did make his way to this future ruled by corporations, and goofy 90s future-slang, his small European dictatorship wasn't enough.
Doom 2099 -- who unlike most alternate future counterparts was indeed our present-day Doom resurrected decades later -- went on a tear. Not one of cartoonish bids for power; this quest for world domination was filled with cold, calculated murder. He started by taking back his own throne, and swiftly moved to steal the largely ceremonial role of the POTUS. You see, when the corporations took over they didn't have much need for a president anymore. So much so they didn't even think to dismantle the position's official power.
Doom, as you might expect, noticed the error. He ousted the U.S. senate (by killing them), and convinced the current presidential puppet to step down (by killing himself).
Murder aside, he was a pretty decent head of state, and a stellar delegator. His impact on other 2099 titles was felt as he roped their various stars into his administration. Every such book in the line adopted the "A.D." suffix. That is, "Anno Doom."
Doom put the X-Men in charge of Halo City -- a burg where humans and mutants lived in peace -- future Spider-Man Miguel O'Hara as Minister of Superhuman Affairs, and the Punisher 2099 as Minister of Punishment, as well as the head of SHIELD. Naturally, the former corporate bigwigs try to remove him, and manage to do just that for a time. Doom being Doom, however, survives the coup and retaliates. Not by getting re-elected, but by disintegrating the lot of them with nanobots.
2. Superman, The Blue Boy Scout in the Oval Office
Tales involving the Blue Boy Scout's ascent to presidency are (usually) much less violent than anything featuring Doctor "Freaking" Doom. Yes, there are multiple stories in which Superman rises to office. And, yes, most of them turn out pretty well for nearly all involved. Superman is Superman, after all. When you give the guiding symbol of what humanity should strive to be some real power things tend to go your way.
Back in the 50s -- long before Elseworlds and alternate futures were around to muck up the works -- one such story of President El was told through the medium of Jimmy Olsen. A bump on the head had Superman's officially licensed pal dreaming of a world where his "two" best friends, Supes and Clark Kent, took over as President and Vice President, respectively. Though it becomes pretty clear which of his two besties Jimmy held in higher esteem, as "Clark" steps down from veep-hood after realizing that he'll never get to sit in the big chair. What with the POTUS being indestructible and all.
On top of all that, Jimmy is reminded that Superman could never be elected President because he wasn't born in the United States. Jeez, Jimmy!
Eventually, we got our first, proper alternate universe with Superman running on the "truth, justice, and the American way" ticket for real. The Armageddon 2001 storyline once again made Superman a just totally super commander-in-chief. This time, however, the book's statement was less sitcom, and more statement. One in which Superman basically turns Earth into a paradise.
Fast-forward to Final Crisis: the multiverse-shattering DC event primarily scribed by Grant Morrison and J.G. Jones. This is our first introduction to Calvin Ellis, a.k.a. Kal-El, a.k.a. Superman. Despite sharing two thirds of a naming scheme this man of steel isn't much like frumpy, dumpy Clark Kent in either of his professions.
Calvin's creation was inspired heavily by president Barack Obama. Like his real-life counterpart he took office, and unlike his fictional double used his alien powers proactively. Such as by disarming nuclear powers and inviting them to the world government. Like any self-respecting Superman he also got to beat up an evil version of himself. Though that was just the first in a string of alternate universe shenanigans that concluded with him leading the multiversal Justice League, Justice Incarnate. This means that of all the theoretical Supermen on this list, Calvin is the one we're most likely to see more of in the future.