In BattleTech and its PC simulator adaptation MechWarrior, BattleMechs with head mounted weapons sometimes have it set up as an eye-beam. The Atlas, which has a skull for a cockpit, can mount a laser in one of the eyes (the other is occupied by the actual pilot), and the Mechwarrior 4 Cyclops has a huge glowing red "eye" where a head should be. You can mount a (light) Particle Projector Cannon there, making it fire lightning bolts
The Beholder is a living embodiment of this trope with its eleven eyes armed with magic rays, as well as various Beholder-kin creatures. There's also lots of creatures with gaze attacks affecting those meeting their eye, such as Basilisk (petrification), Catoblepas (death) and vampires (charm).
And a handful of arcane spells like 'Eyebite' (gaze attacks with minor enchantments like charm or fear), 'Dead Man's Eyes' (caster's eyeballs turn black with white skull-shaped pupils and kills people by looking in their eyes).
Later sourcebooks even provide a Metamagic Feat that allow player characters to store ray spells in each eye for convenient simultaneous blasting for a later date.
The spell Lantern Light from the 3E Book of Exalted Deeds supplement gives clerics and paladins the ability to shoot eye beams.
Forgotten RealmsDwarves Deep got dwarven priestly spell 'Fire Eyes', Seven Sisters added its arcane counterpart — higher-level more powerful, but short-ranged and with bonus heat protection — and 'Basilisk Glare'.
The 3.5E supplement Lost Empires of Faerûn gives the sunmaster Prestige Class the ability to shoot beams of light out of their eyes at 2nd level.
Dragon magazine #46 adventure "The Temple of Poseidon''. Once per minute, the Dark King Ythog-Nthlei can fire four scintillating beams of energy from his eyes that drain Strength from the victim.
The obscenely powerful epic spell 'Vengeful Gaze of God' from the 3E Epic Level Handbook deals anywhere from 305 to 1850 points of damage, the latter value being easily sufficient to kill most deities in one shot, and it has a range just less than two and a half miles. Of course, the massive backlash will likely kill you too.
1st Edition Advanced D&D supplement Fiend Folio. The retriever has 4 eyes that can fire rays up to 60 feet away. Three of them inflict fire, cold and lightning damage (respectively) equal to the retriever's current Hit Points, with a saving throw vs. dragon breath for half damage. The fourth eye can transmute the target into mud, stone, gold or lead (determined randomly).
One of the psychic powers available to the Ork Weirdboy is an eye beam attack, with a strength comparable to the anti-armor melta weaponry used by the Imperium.
The Gaze of Mork is a supercharged laser mounted in the eye of ork Gargants.
In Shadowrun, cybereyes with built in lasers (or projectile weapons) are available. But, it is made very clear that they are very ineffective, especially in combat. In fact, the only effective use is low end tool uses. One alternative, however, is single-use flashbulbs - it won't kill the victims, but rendering them temporarily blind is just as useful.
"Lightning Stare" from GURPS: Magic, which probably isn't a cool as it sounds since you have to make "certain facial motions" in order to cast the spell.
The Champions RPG has a villain named Occulon who has several eye-based powers.
Warhammer fantasy battles likes to use these as magic missiles with gaze of Gork, gaze of mork and Gaze of Nagash as spells with such a name and a description of a light magic spell says that it's a kind of eye beams.
Exalted: Shards of the Exalted Dream has the Empyreal Chaos Charm known as Apocalypse Comet Gaze. This allows Infern - er, Titanic Exalts to, surprise surprise, fire death rays with a glare.
World of Synnibarr is notorious for having bears that attack with these. And it is not even in the top thirty weirdest things about World of Synnibarr.
Arduin RPG, The Compleat Arduin Book 2: Resources Greater Demons.
Iphang, the Lord of the Yellow Horde can fire a brilliant green ray of intense heat from his eye that does 3-60 Hit Points of damage to anything it hits. It has a range of 100 yards and can be fired up once per melee round up to 13 times in a row. After that it can only be fired once per minute until he doesn't use it (allowing it to rest) for 30 minutes.
Karong the Lord of Slime has three large glowing eyes colored red, yellow and green. Once each melee round each eye can send out a beam of its color that is 40 yards long and 5 feet wide. The red ray causes 17-36 Hit Points of burning damage, the yellow ray causes 15-24 Hit Points of immediate rotting damage and 3 Hit Points of continuing rotting damage each melee round thereafter, and the green ray causes paralysis for 1-20 minutes.
Chaosium's supplement All the Worlds' Monsters Volume III
The Shock Troll has two eyes. The grey eye can fire a death ray and the light green eye can fire a Dungeons & Dragons Feeblemind spell.
The Windwalker's gaze causes any creature it looks at to become confused.