Janus

Janus is the god of Choices, Doorways, Beginnings, and Endings. He is a minor god. It is implied he had joined Kronos, but he later obeys Hera.

Appearance
Janus has two faces on one head and looks like a doorman to Percy, Annabeth, Grover and Tyson. It is impossible to look at both faces at once, reflecting on him being the god of choices. His left head is generally a pessimist, and the right head is an optimist.

The Battle of the Labyrinth
Janus appears to Annabeth and causes her great indecision about the choices she has to make. (Later, she tells Percy that the decision had to do with whether or not to trust Luke.) He was also there, thousands of years ago, when the inventor and son of Athena, Daedalus, decided to let his nephew, Perdix, die rather than save him. At the end of the book, he had gone over to the Titans' side. He is never heard of again in the books. He makes Annabeth choose one of two doors. When she is having trouble with her decision, Hera interrupts and Annabeth doesn't have to make her choice.

Trivia
In mythology, Janus is usually depicted as a Latin God of Choices, not Greek.