Every account I’ve read (more recent retcons might have screwed with it, though) says that in Robin’s first case, he snapped a photo of Boss Zucco (the man who’d ordered the murder of Dick Grayson’s parents while shaking down the circus they worked for) shoving one of his henchmen off a building, thus providing the key evidence to send Zucco to the electric chair.
Actually I seem to remember that they decided it was “self-defense–sort of”–which to me meant that the Legionnaires didn’t believe it was either self-defense nor a legal execution, but a majority of them voted to let her back in anyway–probably because they’d hve done the same thing.
The guy’s name was Zucco? Heh. That’s the name of a mob boss on Due South, and one of the more interesting (and serious) recurring villians from that show. 
Self defense was never even floated for Jeckie’s actions. Both times she was called upon to explain her actions - LSH v2 (or 3, depending which count you use) #5 and #26, she says she executed him, challenges anyone to say differently, and nobody ever argues.
The Punisher went to the electric chair for killing Nick Fury. Needless to say, Frank and Nick are both still around…
None spring to mind, mostly because they get put away to fight another day.
I think overall, death by civilized means is not shocking enough, or perhaps too final for the majority of comic book fans and writers. How many times have you seen bad guys “die” only to come back, either as themselves, or in the form of another villain going by the same name?
I was trying to think of moments from one of my favourite short-run series, Marshall Law, but it’s mostly like the earlier Judge Dredd comments. He is authorized by the state to use lethal force, but that’s as close to a civilized execution as things come.
This is especially ironic for the Marshall, who spends the whole of six issues trying to force America’s greatest superhero, The Public Spirit (who deliberatly seems an awful lot like Superman), to admit that he goes around at night raping and murdering women who dress as Public Spirit’s girlfriend - including, at one point, the girlfriend of the Marshall’s civilian alter ego…
… but you’d never guess how it turns out:
[spoiler]The Public Spirit, one of the first superheroes, was sent on a faraway mission to the stars. Because of time dilation, he comes back nearly unaged while everyone else has lived several decades.
When his first wife, the super-siren Virago, becomes pregnant with his baby, he tries to strangle her so that the birth of his son will not cause the space program to select an alternate astronaut. He blames her disappearance on a freak electrical storm that robbed her of her powers and caused her to plunge to her death while they were flying over the ocean.
Unbeknownst to him, Virago survived and gave birth to their super-powered boy. Disguised as the cynical “Mrs. Mallon” and the wheelchair-bound “Danny” (who works as Marshall Law’s assistant at their secret police headquarters), they pull one over on the Marshall, misleading him in his investigation to think PS is the murderer. Since Danny is in fact the murderer and rapist, his DNA would likely lead to conviction of the country’s greatest hero.
After Virago reveals her identity, Danny and the Public Spirit duke it out while the Marshall tries to capture them both. Before he can slap the cuffs on, the Public Spirit is shot in the head by a police sniper under the direction of the Marshall’s boss so that the public won’t learn the truth.
They sweep everything under the rug, and Marshall Law is robbed of the justice he has been so desperately seeking.[/spoiler]
Not quite like Superman, then. 
John Ostrander’s Suicide Squad had similar government cover-ups.
I remember in one of the Captain Marvel comics, from the 1970s revival by DC, Mister Tawny, a museum tour guide, shows the crowd the stuffed body of the alien worm (2 inches long, evil supergenius) Mister Mind, who he said had been put to death by electric chair decades ago. “He was the last worm executed in this state. Also the first.” (Mr. Mind comes back in the same issue, of course.)
I don’t know if that was supported by the original Whiz comics – but here’s a page on the Monster Society of Evil: http://en.wikipedia.org/wiki/Mister_Mind