Cyclops of the X-Men, who has a drawback in the fact that he can't turn it off, requiring him to constantly wear a protective visor, or ruby sunglasses for more casual occasions. Unlike most such characters, his Eye Beams are of concussive (pushing) force instead of heat (though some writers seem unaware of this), affectionately referred to as PUNCHES FROM THE PUNCH DIMENSION by fans. As a result he is one of the few eye-beam heroes who can choose to merely knock you out by looking at you, as well as having the option to put holes in you.
And ever since then, there's been plenty of Shout-Out whenever an actual Cyclops shoots Eye Beams of one type or another.
Superman's famous heat vision, which he usually uses as a "utility power" for things like escaping something, freeing someone, or other uses. If he ever uses it as a weapon against an enemy, it's usually against a robotic or other nonliving enemy (because Superman adheres to Thou Shalt Not Kill). Him using this power is also usually a sign that you've trulypissed him off.
Superman (to Mongul): Burn.
In the Silver Age, Superman had to wear glasses made from Kryptonian glass in order to use his heat vision while disguised as Clark Kent (otherwise the glasses would melt); Post-Crisis, this power was reinvented as pyrokinesis and thus that's not necessary anymore. Naturally, the TV versions tend to simply discreetly move his glasses out of the way.
Originally, the heat effect was just supposed to be his X-Ray vision turned up full blast, so for most of the Silver Age it was always described as "using the heat of my X-ray vision." The phrase wasn't shortened to "heat vision" until almost the start of the Bronze Age. Post-Crisis, his heat vision has been considered a separate power from his X-Ray vision.
Post-Crisis, Superman's use of heat vision changed markedly, as he was now a solar-powered superhero. Using heat vision came out of the same energy bank that all his other powers used, but at a very steep cost. Now heat vision was used sparingly or only once a battle. Really cutting loose with the beams now means that Supes is NOT in his happy place.
Remember that bit in the cinematic trailer of DC Universe Online? He MELTED Black Adam's face off with only a guttural yell. Scene in question
Power Girl isn't quite as restrained in her use of heat vision as Big Blue. When Satanna (mad scientist / surgeon) kidnaps her best friend to experiment on her, PG blasts her arm off. She then tells the horrified Satanna that she can pick it up and reattach it after telling her where to find Terra.
The Homelander, The Boys' Captain Patriotic Expy of Superman has them, which he uses to discipline fellow superheroes and take down airliners. Billy's wife died when a superfetus used its Eye Beams to get out of her womb, killing her (and making the Homelander the most likely candidate for Billy's wife's rapist).
Black Noir has these as well since he's an even stronger clone of the Homelander. He's also the one who really raped Becky.
Apollo, from The Authority, has these—makes sense as he's a Superman homage. In the story where he's introduced, writer Warren Ellis tries to Hand Wave this as saying he's got "weird eye structure" which can cause light to lase.
The eye beams of the 1990s Marvel character Sleepwalker, known as his "warp beams", can be used to alter the physical shape, and to a lesser extent the physical characteristics, of anything he hits with them. Ironically, living entities are the only things Sleepwalker tries not to use his warp vision on, because of the horrible effects his beams can have on them.
Painfullydeconstructed in the comic Archaic: it kills the character's enemies but also destroys his eyes.
The titular superhumans of Uber can generate powerful "disruption halos" from their eyes. For standard Ubers, these halos manifest as webs of crackling energy, and are extremely powerful but short-ranged. The most powerful Ubers, however, can fire continuous beams of destruction to wipe out whole armies at kilometer ranges.