Just about all I know about Superman and Batman I’ve learned (or mis-learned) at the movies. But in the comics, have politics ever been an issue? Have there been candidates for mayor of their respective cities, or ballot initiatives, that have drawn the superheroes’ attention? For instance, candidates they knew to be dangerous/crooked/affiliated with supervillains, who had to be kept out of office at all costs? Have state (whatever state those cities are in) or even national politics ever been featured, even if only in passing, in any Superman or Batman comics?
Lex Luthor was elected president, so I imagine that was featured pretty prominantly in Superman (and other titles).
And Nancy Reagan is an android Manunter spy.
Yeah, for the longest time in the comics, Lex Luthor was known to the world as the brilliant and innovative CEO of the giant LexCorp corporation, a leader in high technology among other things, and also as a philanthropist around Metropolis and the world. He kept his evil schemes and plots against Superman pretty quiet, and fooled the public into electing him President (forcing Superman to occasionally acquiesce to his orders as a result). I thought it was a fascinating twist, myself, and the ramifications of the Luthor presidency were felt throughout all the DC Universe comics.
I think during Mark Gruenwald’s run on Captain America, the leader of the sinister Secret Empire was revealed to be the current U.S. President (not sure which one, and he was never actually shows), but he killed himself at his desk before Cap could expose him. I’ve never actually read this, so hopefully an old-school Marvel fan will be along soon enough.
In The Authority, the team of violent liberal-intentioned superheroes with fascist tendencies killed the corrupt U.S. president (an obvious G.W. Bush analogue) and took over the United States themselves during the “Coup D’Etat” storyline.
It was strongly implied to be Richard Milhouse Nixon.
And there have been a couple of times in which Gotham’s Mayor wanted to have Batman busted.
Batman: Year One also deals with political corruption in Gotham.
Wasn’t Batman upset with Superman being used as a political puppet in Dark Night Returns?
Yes, which is odd because Superman’s never been a government stooge except during the same eras where Batman was. In his early days, Superman was a leftist dynamo. Intimidating munitions makers and slumlords. Now he’s a more apolitical do-gooder, but still willing to take on the man when the situation demands.
For one, Batman had somehow managed to become even more cynical by the time of DKR and for two, DKR isn’t canon.
When the Batman comic began in the late 1930s, the memory of Prohibition was still fresh, and how gangsters like Al Capone had been able to pay off the police. Political machines still ran many city governments and some were widely reputed to have organized crime ties. While the police aren’t (usually) Batman’s enemies, the strong implication is that the rampant crime in Gotham is due to the police force being corrupt, with the major exception of Commissioner Gordon himself. It’s also been strongly implied that Gordon secretly supports the Batman because Batman can clean up Gotham the way Gordon isn’t allowed to do.
The office of Police Commissioner in Gotham City is something of a major point at times - Commissioner Gordon is rather friendlier to the capes than his predeccessor, Loeb, or Akins, who came in for the year or so that Gordon was retired. Apparently, he’s also better able to keep down the insipient corruption of the GCPD than either Loeb or Akins. (Assuming either of them actually tried at all.)
In a related cameo, one issue of Captain America in the mid '80s had Cap running around Washington DC one night, as the Serpent Society went around poisoning the residents with some venom that turned ordinary folks into fang-toothed green-scaled hissing zombies. Cap chases one of the Society members to the White House, but is then attacked by an infected Ronald Reagan, hissing “Mommy!” all the while. 
I think Gruenwald wrote that one, too.