Lucy Liu's head

Lucy Liu's Head is the head of 21st century actress Lucy Liu. For much of her life, Liu has been at Kidnappster, where they have been holding her prisoner for 800 years. During this time, many people downloaded illegal copies of her. After being rescued by Bender, Liu began a relationship with him, and was last seen living inside Bender. Her current status is unknown.

Liubot
The Liubot was a computer-generated duplicate of Lucy Liu that was downloaded by Fry. Later, a swarm of them were sent to kill the Planet Express crew by the Kidnappster CEO after Bender stole Lucy Liu's Head from the company. After the attack, it is believed that all Liubots were destroyed.

Trivia

 * Lucy Liu recorded some lines in advance for a future episode.
 * Liu was apparently inside Bender during the Roswell incident, though Bender may have taken her out of his chest before that episode and put her back before her next appearance. It is also possible she was in his chest cavity during the events of Bender's Big Score. Luckily heads survive in jars indefinitely, assuming they are fed.