Buddha (yes, the founder of Buddhism himself) was said, after being denied access to the scrolls at a temple, to have sat down and stared at the wall until a hole was burned into it. The monks caved in and gave him full access after that. Considering the realism in most of Buddha's stories, this stands out quite a bit, although it's nothing compared to most of too-Anime-for-Goku higher mythology.
Older Than Print: Before the Tuatha De Danaan moved into Ireland in Celtic Mythology, the giant Fomor were led by Balor of the One Eye, whose deadly gaze could burn men "like leaves cast into a forge." When Balor was slain by his grandson Lugh, he fell face first to the ground with his eye still open, and burned a hole into the ground. It's still there today, as a lake.
Another version of the above myth has Balor's eye bashed out the back of his head, casting its deadly gaze on his own army. Needless to say, they didn't win.
Shiva got an extra eye when gods tried to make him stop mourning for Sati and marry Parvati (he didn't know she's the reincarnation of his ex-wife, and no one thought to tell him). He opened his two eyes, noticed her, the god of lust Kama shot Shiva with a bow to stir up passion in him (sounds familiar?)... and then the plan backfired: to everyone's surprise he opened a third eye and incinerated Kama with an eyebeam (Parvati found another way to become his wife and asked him to resurrect Kama). Scorching gaze of annoyed ascetics is a recurring motif for Hinduism, but mortals' anatomy doesn't change.
The basilisk was held to have eye beams of pure death, causing instantaneous death to any caught in its gaze. Another take on the myth is that the victim is betrayed by their own vision, and dies when they behold the creature. Still others hold a combination of the two, and eye contact between monster and victim is required.