In the answer to my other question : Why aren't all Professors Ravenclaws? it was pointed out that Hogwarts Professors might be from any House. In actuality, were there an equal number of Professors in each House, or were the number skewed in favor of any House? Any official source (in particular, Pottermore) is acceptable to establish which House any person was in.
Totals (including 4 founders):
24 - Unknown (including 3 unnamed Headmasters) 7 - Unknown and not even 100% were in Hogwarts despite title Professor 6 or 8 - Slytherin (Carrows were unknown but likely S) 6 - Gryffindor (3 of them during Harry's time) 5 - Ravenclaw 2 - Hufflepuff 1 - Didn't attend Hogwarts (Firenze) 1 - Non-Slytherin (unknown otherwise)
In 2 cases - Carrows - the house isn't known from canon but can be guessed easily.
I would also theorize that Arithmancy professor was likely Ravenclaw despite being listed as unknown officially.
4 people listed are Headmasters of Hogwarts without 100% canon info that they were Professors. Purely theoretically, it's possible they could have held the post without being Professors.
I listed both Alastor Moody and Barty Crouch Jr as separate people. Alastor never taught while Barty wasn't invited to be a Professor.
I have prepended them with their house if known.
I didn't bother including the 4 founders in this list but included them in the totals above.
G Albus Dumbledore Transfiguration, Unknown-1956 S? Alecto Carrow Muggle Studies, 1997-1998 ? Alastor Moody (didn't get to teach) S? Amycus Carrow Dark Arts, 1997-1998 non-S Armando Dippet (Headmaster) ? Aurora Sinistra Astronomy ? Bathilda Bagshot (Hermione refers to her as Professor) ? Bathsheda Babbling Study of Ancient Runes S Bartemius Crouch Jr Defence Against the Dark Arts, 1994-1995 R Basil Fronsac (Mid-19th century headmaster) ? Brutus Scrimgeour ?? Catullus Spangle (Called Professor but not certain he taught in Hogwarts) ? Charity Burbage Muggle Studies, 1993-1997 ? Cuthbert Binns History of Magic S Dolores Umbridge Defence Against the Dark Arts, 1995-1996 ?? Emerett Picardy ? Emeric Switch (textbook author) ? Eupraxia Mole (Headmistress) R Filius Flitwick Charms N/A Firenze Divination, 1995-1997 ? Fytherley Undercliffe (Headmaster) ? Galatea Merrythought Defence Against the Dark Arts, 1895-1945 R Gilderoy Lockhart Defence Against the Dark Arts, 1992-1993 ?? Griselda Marchbanks (Called Professor by JKR but not certain she taught in Hogwarts) ?? Helbert Spleen (Called Professor but not certain he taught in Hogwarts) ? Herbert Beery Herbology S Horace Slughorn Potions Professor, 1942-1981 and 1996-Unknown ? Limebert (Headmaster) ?? Marlowe Forfang (Called Professor but not certain he taught in Hogwarts) G Minerva McGonagall Transfiguration, 1956-1998 G Neville Longbottom Herbology, Before 2017-Unknown S Phineas Nigellus Black (Headmaster) ?? Phoebus Penrose (Called Professor but not certain he taught in Hogwarts) H Pomona Sprout Herbology, Unknown-Before 2017 ? Quentin Trimble R Quirinus Quirrell Muggle Studies until 1990; DADA ?? Regulus Moonshine (Called Professor but not certain he taught in Hogwarts) G Remus Lupin Defence Against the Dark Arts, 1993-1994 ? Rolanda Hooch Flying Instructor G Rubeus Hagrid Care of Magical Creatures, 1993-Unknown ? Septima Vector Arithmancy S Severus Snape Potions, 1980-1996, DADA ? Silvanus Kettleburn Care of Magical Creatures, Unknown-1993 ? Swoopstikes ? Sybill Trelawney Divination, 1979- unknown ? Tofty (Called Professor but not certain he taught in Hogwarts) ? Vindictus Viridian Unknown, possibly Potions in 1703 ? Wilhelmina Grubbly-Plank Care of Magical Creatures ? Male Muggle Studies teacher Muggle Studies, 1990 - 1993 ? 3 unknown Headmasters
A complete list, broken down by house and with canon sources. But for the impatient, here’s the tl;dr, in a pretty chart:
Hufflepuff gets pretty short thrift here.
Here’s the breakdown, with houses sorted alphabetically:
Godric Gryffindor, by virtue of being the founder.
Minerva McGonagall. She was head of Gryffindor in Harry’s time, and per J.K. Rowling’s old website:
Yes, if the teacher is Head of House you can indeed assume that they were pupils within that house.
Alternatively, we could look at her Pottermore entry:
After five and a half minutes, the Sorting Hat, which had been vacillating between the houses of Ravenclaw and Gryffindor, placed Minerva in the latter.
Albus Dumbledore. Per Hermione’s helpful comments on the train:
“I’ve been asking around and I hope I’m in Gryffindor, it sounds by far the best, I hear Dumbledore himself was one.”
— Philosopher’s Stone, chapter 6 (The Journey from Platform Nine and Three-Quarters)
Remus Lupin. We witness his sorting, see memories of him in Gryffindor with James, and have a J.K. Rowling quote to back it up. See my answer to https://scifi.stackexchange.com/a/54300/3567 for details.
Rubeus Hagrid. I can't remember if this is confirmed in the books (fairly sure), or J.K. Rowling addressed this in a web chat:
What house was Hagrid in?
Hagrid was in Gryffindor, naturally!
Neville Longbottom. We learn in the epilogue that he’s taken up the position of Herbology professor:
“Outside, yeah, but at school he’s Professor Longbottom, isn’t he? I can’t walk into Herbology and give him love….”
— Deathly Hallows, epilogue (Nineteen Years Later)
We witness his sorting, and essentially his entire Hogwarts career as a Gryffindor.
Helga Hufflepuff, by virtue of being the founder.
Pomona Sprout. She was head of Hufflepuff in Harry’s time, so per J.K. Rowling’s comment above, must have been in Hufflepuff when she was at school.
Sylvanus Kettleburn. He taught Care of Magical Creatures before Hagrid, and his Pottermore entry tells us that he was sorted into Hufflepuff.
Rowena Ravenclaw, by virtue of being the founder.
Filius Flitwick. Head of Ravenclaw in Harry’s time, so must have been Ravenclaw while at school.
This is backed up by Professor McGonagall's Pottermore entry, which mentions an amusing coincidence between the two:
The Sorting Hat, which had been vacillating between the houses of Ravenclaw and Gryffindor, placed Minerva in the latter (in later years, this circumstance was a subject of gentle humour between Minerva and her colleague Filius Flitwick, over whom the Sorting Hat suffered the same confusion, but reached the opposite conclusion.)
Gilderoy Lockhart. Per his Pottermore entry:
Sorted into Ravenclaw house, Lockhart was soon achieving good marks in his schoolwork, but there was always a kink in his nature that made him increasingly unsatisfied.
His HP Wiki entry also mentions an appearance in Ravenclaw robes in promotional material for the films, but I haven't checked that.
Quirinus Quirrell. In his Pottermore entry, his house is listed as Ravenclaw. We don’t get any more detail than that.
Basil Fronsac. Former headmaster of Hogwarts (dates unknown), he appears in several of the video games. I don’t know if he explicitly states that he as sorted into Ravenclaw, but he talks about wanting to help “inquisitive minds”, and asks you to find out where Rowena Ravenclaw came from as a mini-task.
Salazar Slytherin, by virtue of being the founder.
Severus Snape. Head of Slytherin in Harry’s time. We also witness his sorting, via a memory in the final book:
Harry walked with [Snape] to the stool, watched him place the hat upon his head. “Slytherin!” cried the Sorting Hat.
— Deathly Hallows, chapter 33 (The Prince’s Tale)
Horace Slughorn. When he first meets Harry, he tells Harry that he used to be head of Slytherin, and we can apply the same reasoning as before:
“Which was your house?”
“I was Head of Slytherin,” said Slughorn.
— Half-Blood Prince, chapter 4 (Horace Slughorn)
Dolores Umbridge. At an event about The Casual Vacancy, J.K. Rowling was asked about Umbridge’s house, and the result was reported on Twitter:
Breaking! HPA staffer Kaci asked Jo what house Umbridge is in. Verdict: Slytherin. #JKRlive
— @TheHPAlliance on Twitter, October 2012
Phineas Nigellus Black. Former headmaster of Hogwarts. He was related to Sirius, and we know that almost all of the Black family were sorted into Slytherin. Alternatively, his portrait is painted with Slytherin colours:
“He says he’ll be delighted,” said a bored voice behind Dumbledore; the wizard called Phineas had reappeared in front of his Slytherin banner.
— Order of the Phoenix, chapter 22 (St. Mungo’s Hospital for Magical Maladies and Injuries)
Alecto and Amycus Carrow. There's no canon mention of this, but as Death Eaters, I feel pretty confident in saying that they'd both be in Slytherin.