Hogwarts doesn't just host living people, but also dead people! There is a ghost for every house, as well as other ghosts without a signature house. 

 Gryffindor's Ghost's name is Sr. Nicholas, but is known by every student as Nearly Headless Nick. Nearly Headless Nick was left nearly headless after an improper execution. While he lived, he served in the Royal Court. He offered to straighten a woman called Lady Grieve's teeth for her, but it backfired and she grew tusks and he was sent to be executed. But while he was a child, he went to Hogwarts and became a Gryffindor. He was one of the very few who chose to come back as a ghost, and was then made Gryffindor ghost.

Slytherin's Ghost's name is the Bloody Baron. He went to Hogwarts while the founders were still alive, and was sorted into Slytherin. After he graduated, he fell in love with Rowena Ravenclaw's daughter, Helena Ravenclaw. When Helena stole her mother's diadem, Rowena sent the Bloody Baron to find her and convince her to come home and return the diadem. When Helena refused, the Bloody Baron killed her in rage, and then was so ashamed of himself he ended his own life. 

 Ravenclaw's Ghost is Helena Ravenclaw, Rowena Ravenclaw's daughter. While alive, she attended Hogwarts and was sorted into Ravenclaw. After she graduated, a man called the Bloody Baron fell in love with her. When she stole her mother's diadem to enhance her intelligence, Rowena sent the Bloody Baron to convince Helena to come home, but when Helena refused, the Bloody Baron killed her. Her mother died not long after.

Hufflepuff's Ghost is called the Fat Friar. A very kind man, he attended Hogwarts and was sorted into Hufflepuff. He was very religious and attended a Muggle church. But senior churchman became suspicious because he could cure the pox merely by poking pheasants with a stick. He was soon executed and came back as the Hufflepuff ghost. 

Moaning Myrtle is a ghost that haunts the girls bathroom on the second floor. She was the Muggle-born that was killed when Tom Riddle opened the Chamber of Secrets. At the time of her death, she had been crying in a bathroom stall because a girl named Olive Hornby was teasing her about her glasses. Then, she made eye contact with the basilisk and was killed. Later, Olive came back in the bathroom and found her.