Nappster is a company on the internet. They specialize in Celebrity personalities, which people can install onto Blank Robots. In I Dated A Robot, Fry downloaded Lucy Liu's personality and put it in the form of LiuBot. He dated her until her death near the end of I Dated A Robot.
The company's real name is KidNappster, as shown when a sign breaks in the Headquarters.
As shown by the Nappster blimp, the URL is nappster.com.
Nappster is a parody of Napster, a peer-to-peer (P2P) file sharing Internet software created in 1999.