Theseus and Pirithous

Theseus and Pirithous fight a centaur attempting  to steal a bride from a wedding party

Thousands of years before there were "Buddy Films" in Hollywood, such as the "Lethal Weapon" series, "Men In Black", etc, there was Theseus and Pirithous.

Pirithous was said to be a prince of Lapith. Having heard much of Theseus, he decided to test the Athenian's mettle by stealing his cattle. When Theseus showed up in hot pursuit, the two men faced off…and found they liked each other. And thus began a friendship that was akin to that of Achilles and Patrocles. Theseus and Pirithous were brothers thereafter and fought shoulder-to-shoulder, battling drunken Centaurs at a wedding party, kidnapping a young Helen of Troy, and even raiding the realm of Hades to steal his bride, Persophene.

Though one of the first, the buddy story of Theseus and Pirithous was not the first. 

That nod goes to "The Epic of Gilgamesh". Taken from cuneiform tablets, it is the possibly the earliest work of literature known to man. 

Gilgamesh, the king of Ur in ancient Mesopotamia, seeks to capture a "wild man" called Enkidu. Enkidu was created by the gods to counter the powerful Gilgamesh because they feared his strength. But instead of a counter to the burgeoning might of men, Enkidu and Gilgamesh become best friends. When the gods kill Enkidu because Gilgamesh spurns the advances of a goddess,  Gilgamesh embarks on a quest to defeat death, and encounters Noah and his wife, the only two people the gods granted immortality (The story of God, Noah, and the Ark predates the Bible). Gilgamesh finally learns that the lot of man is death, and comes to terms with it.