Note: Unlike the rest of this site, these people will be in the order they retired, not alphabetically.
Professor Armondo Dippet - Former Headmaster. Dippet was Headmaster when Dumbledore was Transfiguration teacher over 50 years ago. He managed to keep the school under control when the Chamber of Secrets was opened the first time.
Professor Quirrell - Former Defense Against the Dark Arts teacher. Quirrell was teaching during Harry's first year at Hogwarts. He was always seen wearing a large turban. No one knew, however, that underneath the turban Quirrell was hiding the face of Lord Voldemort himself. At the end of the year Harry faced offf against Voldemort. Voldemort escaped, but Quirrell was killed.
Professor Gilderoy Lockhart - Former Defense Against the Dark Arts teacher. Lockhart taught in Harry's second year. Lockhart made a name for himself by finding people who did amazing things, then erased their memories. However, as a teacher, he didn't know much. His career ended when he accidentely erase his entire memory.
Professor Kettleburn - Former Care of Magical Creatures teacher. Not much is known about Kettleburn, except that he retired "to spend some time with his remaining limbs", whatever that means.
Professor Remus Lupin - Former Defense Against the Dark Arts teacher. Lupin taught in Harry's third year. Lupin made up for much of the stuff people didn't learn under Lockhart. However, he had to stop teaching when a teacher (Snape) let it slip that Lupin was a werewolf. Lupin had to flee to escape the wrath of parents. Many students liked having Lupin as a teacher, and want him to return.
Professor Alastor (Mad-Eye) Moody - Former Defense Against the Dark Arts teacher. A great Auror in the days of Lord Voldemort, Moody was asked by Professor Dumbledore to come out of retirement to teach during Harry's fourth year. Moddy is known for being very cautious about people coming to kill him, so he has a magical eye that can see through walls, wood, even invisibility cloaks.