Identity

Ideas concerning identity and what it means to be oneself are a recurring theme on Futurama.

Rebirth
This episode is heavy with identity-related ideas.

At the beginning, the entire crew except Farnsworth are killed, as well as Zapp and Kif. Their bodies are revived via Farnsworth's stem cell vat. They seem to remain the same persons that they were before, that is, they aren't obviously zombies or anything strange.

Fry makes a robot-Leela and Leela makes a robot-Fry. Both robots spend some time believing that they are the originals. Twice during this episode, Robot-Leela can be found musing on the meaning of identity and the nature of consciousness.

The new Fry who appears at the end of the episode isn't simply revived as the others are. Their heads stayed intact, so they are presumably the same persons as before. But Fry's brain was destroyed: the person who comes out of the stem cell vat is a clone of the dead Fry. In other words, through Farnsworth's miracle of science, this person is a copy of the original Fry in every sense that the robot was a copy of the original Fry. It is notable that no one seems concerned about this.

When Farnsworth finally tells the whole story and Leela learns that Fry is dead, she says, "My god, I can't believe I'll never see that particular Fry again." This is an important point concerning personal identity: the original Fry has passed away.