In Krypton No More, Superman uses his heat vision in very varied ways such as warming himself up after a freezing attack or blasting Protector as he is changing his molecular structure.
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). 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 during the 1950s and early 1960s, it was always described as using "the heat of my X-ray vision." Heat vision finally became a separate power in 1961's Action Comics #275, and has stayed such since. (Some Silver Age and Bronze Age reprints of stories using the earlier phrase would awkwardly reword it as "the rays of my heat vision" or similar.)
The above is also why during the Silver Age, Superman's heat vision was canonically invisible to ordinary humans and only drawn in so that the readers could see that he was using the power. On at least one occasion, Superman identified a human-like non-human by her revealing that she could see the rays of Superman's heat vision and not just its effects.
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.
In the cinematic trailer of DC Universe Online, He MELTED Black Adam's face off with only a guttural yell. Scene in question
In Superman vs. the Amazing Spider-Man, Spider-Man calls Superman's heat vision your eyeball rays. Superman uses them to end his first battle against Lex Luthor quickly: he melts a bulkhead wall of Lex's submarine. So Luthor has only two options left: stop fighting and allow Superman capture him, or drown. In this story, Lex Luthor's Superman decoy is equipped with eye beams that teleport their target.
In Kryptonite Nevermore, Superman tries to stop a hijacked plane by fusing its electrical system with heat-vision... which chooses that precise moment to fail.
Some examples from Superman: Brainiac: Superman uses his heat vision when he runs into a Brainiac's mechanical soldier. Kara's heat vision activates when she stares at a Brainiacs probe and remembers Kandor's abduction, and her heat beams melt the androids head. Brainiac's robots' eyes fire electrical, white-and-red beams. And Superman also uses his optic beams to cut off the wires connecting Metropolis and Kandor to Brainiac's ship.
In "The Supergirl From Krypton" Superman unleashes his heat vision's full power against an army of defective Doomsday clones, incinerating them instantly.
It's revealed in the New 52, that Superman can hurt himself with his beams. Seen when Lex Luthor needed Supes's blood and Clark obliged◊
Supergirl's own heat vision is her best and most used weapon.
In the Red Daughter of Krypton arc Kara blew spaceships up, boiled a tsunami off and burned Worldkiller-1's host body out with it.
Bizarrogirl's eyes can fire freezing beams. She also has stone vision to contrast Supergirl's X-Ray vision, something that no other Bizarro has.
Power Girl isn't quite as restrained in her use of heat vision as Big Blue or the Girl of Steel. 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.
Martian Manhunter has his Martian Vision. The effect of which depends on the writer, ranging from heat, disintegration or concussive force. And once, memorably, for making ice cream. Rather confusing since Manhuter has a psychosomatic fear of fire and yet he can cause flammable objects to catch fire with his eyes. But it seems nearly all Flying Brick(s) have to be able to use eyebeams to hang tough with Superman.
And when we say "travel any path" we mean travel any path. One of the most striking features of Darkseid's Omega Beam is that it rarely every curves to change direction or moves straightforwardly at all, instead making sharp angles, even at degrees less than 90.
Scott Summers' optic blasts have a drawback in the fact that he can't turn them off (thanks to a head injury he got as a kid) 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. He's also a relatively rare character who has this power and is explicitly noted to be immune to the effects, so even if a Deadly Dodging enemy tricks him into shooting himself it has no affect beyond possibly knocking him off his feet (and being really embarrassing).
And ever since then, there's been plenty of Shout-Out whenever an actual Cyclops shoots Eye Beams of one type or another.
Interestingly when Roguetakes Cyclops's power, she can usually turn the beams off and on with ease; something Scott is unable to do.
In the Astonishing X-Men run, Scott decided to let loose on a Sentinel that was wrecking everyone. Instead of retreating to safety Cyclops stated "I want this thing off my lawn", and what came next was entire panel of just red◊ until Scott puts his visor back on. Even Wolverine, who normally disrespects Cyclops, was humbled.
Logan: Every now and then Summers... I still remember why youre in charge.
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.
Hyperion, being a Superman Expy, naturally has the ability shoot energy beams from his eyes. Since he's often an Anti-Hero or outright villain, he's a lot more prone to using them on living targets.
Painfullydeconstructed in the comic Archaic: it kills the character's enemies but also destroys his eyes.
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.
Black Moon Chronicles: Wismerhill gain the ability to shoot red beams out of his eyes because he's a half-demon.
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.
Slightly deconstructed in Gold Digger with D'ebra. As a Platinum Dragon, she can fire eyebeams, but trying to do so in her human form hurts her eyes because, surprisingly, Human eyes are not made to channel concentrated Ether. If she has to do eyeblasts in human form, she usually uses a spell to cover her eyes with magic lenses that can focus the energy better.
Vermin the Cybernik of Sonic the Comic has them, and even calls them Eye Beams, Super Sonic also has eye beams and Robotnik when he has the power of Chaos Emeralds has Eye Beams as one of his powers.
In Strikeforce: Morituri, this was the ability that Woodrow Green of the first group of Morituri subjects received.
The titular superhumans of Über 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.