The legend of Theseus and the Minotaur follows a pretty classic pattern. Some awful monster is off doing something bad somewhere, so some hero has to go kick its butt. A ton of this kind of behavior definitely goes on in other Greek mythology. For example, Theseus's famous great-grandfather, Perseus, slew Medusa and the Cetus, a sea monster. Then, of course, there's Heracles who slew the Hydra, the Nemean Lion, and about a billion other things.
The Greeks were definitely not the first people to come up with this whole hero slays monster thing either. The oldest example is from the The Epic of Gilgamesh.
This super ancient Sumerian epic tells of the warrior-king Gilgamesh, who slew all sorts of stuff--probably most famously the monstrous demon, Humbaba. Of course, the Minotaur is like a little baby monster compared to Humbaba, who was gigantic and could spew fire and floods from his mouth. Also, Humbaba's face was supposed to be made of entrails, which is about as monstrous as it gets.
The list of monster slaying heroes that came after Theseus is pretty much endless. The oldest surviving example from English literature comes from the epic of Beowulf. In this ancient poem, Beowulf slays the monstrous Grendel, Grendel's vicious mother, and a terrible dragon . Throughout the centuries, dragons were pretty popular creatures for heroes to slay. The story of St. George and the Dragon is one pretty popular one. In this tale, the heroic St. George who slays the horrible dragon, who like the Minotaur has a taste for young virgins.