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 PUNCHES FROM THE PUNCH DIMENSION concussive (pushing) force instead of heat (though some writers seem unaware of this). 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.
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.
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.
On the Marvel side with a similar character, Thanos of Titan has eye beams that seem to be similar to but more powerful than the energy blasts he shoots from his fists.
An example from Grant Morrison: in his 2000 series Marvel Boy, employees of Hexus the Living Corporation would sacrifice their own body heat to fire lasers from their eyes—becoming desiccated corpses in the process.
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.
