Regular Teachers
Professor Albus Dumbledore - Former Transfiguration teacher, Headmaster of Hogwarts
Professor Binns - History of Magic (only ghost teacher)
Professor Filius Flitwick - Charms, Head of Ravenclaw House
Professor Rubeus Hagrid - Care of Magical Creature, Keeper of Keys and Grounds at Hogwarts
Madam Hooch - Quidditch Coach / Flying Instructer
Professor Minerva McGonagoll - Transfiguration, Head of Gryffindor House, Deputy Headmistress
Madam Poppy Pomfrey - Nurse
Professor Sprout - Herbology, Head of Hufflepuff House
Professor Severus Snape - Potions, Head of Slytherin House
Professor Sybill Trelawny - Divination
Professor Sinistra - Astronomy
Professor Vector - Arithmancy
Madam Irma Pince - Librarian
Substitues
Professor Grubbly-Plank - Care of Magical Creatures
Firenze (centaur) - Divination (after Trelawny got sacked)
Defence Against the Dark Arts
Professor Quirell - Dead, after being posessed by Lord Voldemort
Professor Gilderoy Lockhart - Phony book writer, lost his memory from backfiring spell
Professor Remus Lupin - Werewolf, resigned.
Professor Alastor Moody, aka Barty Crouch Jr. - B.C. Jr. took over Moody's job using the polyjuice potion, and tried to kill Harry
Professor Dolores Umbridge - Assigned by the Ministry of Magic, was almost killed by centaurs
Other
Argus Filch - Caretaker
The house elves
Ghosts and other characters
Sir Nicholas de Mimsy-Porpington, aka Nearly Headless Nick - Gryffindor ghost
The Fat Friar - Hufflepuff ghost
The Grey Lady - Ravenclaw ghost
The Bloody Baron - Slytherin ghost
Peeves - school poltergeist
The Fat Lady - Portait, entrance to Gryffindor tower.
Sir Cadogan - Temporary replacement for the Fat Lady in bk. 3.
Fang - Hagrid's trusty Boarhound