Strangely enough, eye beams are rarely seen as a commodity in this very energy-based series. The only characters out of the Loads and Loads of Characters who exhibit the ability are Piccolo, Nappa, Frieza, Cooler, Dr. Gero, Androids 16 and 19 and Cell.
Namekians use it a lot: Piccolo, his father King Piccolo, and later Lord Slug.
Tien also used them in the original series. He shots them out of his third eye.
An enraged Goku uses eye beams on a rock formation to bury Vegeta after the latter was killed by Frieza. It's the only time we see him do this.
Daizenshuu 7 claims that eye beams are different from the Ki Attacks used in the series, and Dr. Gero's and Android 16's are different from that.
In The Sigh of Haruhi Suzumiya, the arc that depicts the filming of the fictional movie shown in that episode, the eye beams were for real, and nearly killed Kyon at least once. Even Nagato Yuki was caught unaware at how many types of Eye Beams Haruhi can imagine.
It should also be noted that the first manifested Mikuru Beam behaved like an actual cutting laser.
Subverted in The Five Star Stories. The first time the colossal Jagd Mirage uses its eye lasers it ends up burning out its main cameras.
Afghanis-Tan has Meriken suddenly pull these out to attack Afganis after being bitten by her cat Al-Nyaida. If you haven't figured this out already, this is the comic's portrayal of 9-11 and the subsequent invasion of Afghanistan.
Stroheim also gets one that fires concentrated Ultraviolet Light. It proved to be extremely effective against creatures weak to sunlight, and backpack-mounted versions were later manufactured and distributed to foot soldiers.
In School Rumble, the freakishly huge head editor of where Harima's manga is being published has Eye Beams as well.
In Rebuild of Evangelion 2.0: You Can (Not) Advance, Unit 01 does this during the Zeruel battle when Shinji becomes pissed enough. Interestingly, it behaved like an actual beam rather than Zeruel's "deadly gaze" (i.e. its eyes twinkle, then the target is blow to hell and back with Creepy Cool Crosses).
Speaking of Zeruel, other angels in Neon Genesis Evangelion have access to eye beams. Sachiel has the same "deadly gaze" that Zeruel has, complete with cross shaped blasts, and Israfel Kou and Otsu can both shoot simple eye beams.
The other two bigs, Big Fou and Big Duo also sport these. At the end of the series, Big Duo even gets its upgraded.
In Shinzo Mushrambo was able to instantly incinerate a mook with black fire just by glancing in his direction. He was of course evil and brainwashed at the time but that didn't change how powerful he was so chances are he could still do it.
In Digimon, the eyes are as good a place as any from which to launch one's beam attacks, but special mention goes to Duskmon. His suit has eyes on it at various places, and his Deadly Gaze attack involves all of them focusing on you and firing death ray. Using this attack at far less than full strength can put Mons of higher levels in their place (and a Digimon being able to take on a higher-leveled one is extremely rare. If you don't count the clear Worf Had the Flu situations, you can count on one hand the times it's happened in franchise history. Dusky was something of a Game-Breaker.)
Metalgarurumon, Monzaemon, Shakkoumon, and Nefertimon all had Eye Beams as at least one of their abilities.
Let's not forget Pegasus and Bakura's Shadow Game from Yu-Gi-Oh!: Ancient Egyptian Laser Beams!
On Pokémon, this is how the move Foresight is often rendered. It doesn't cause any damage, but it does dispel illusions and reveal Ghost Pokémon while making them vulnerable to Normal and Fighting attacks.