Note: I haven't actually seen/read/heard every single companion in the Whoniverse, so I'm sticking to the characters I know best. Sorry, Dodo fans.
GryffindorThe house known for its bravery and for producing such figures as Harry Potter, Dumbledore, Hagrid, and Sirius Black. Many of the ones I put in here are warriors--Captain Jack Harkness (9-10), Brigadier Lethbridge-Stewart (2-5, 7), Jamie McCrimmon (2), Leela (4), and Ace (7). Some you'd never want to get on their bad side, namely Tegan Jovanka (5) and Donna Noble (10), the later of which would be in Gryffindor by default as she is obviously a Weasley. Others display an adventurous spirit: Sarah Jane Smith (3-4), always eager to get to the bottom of a story; Romana's second regeneration (4), who goes off by herself into E-Space; Bernice Summerfield (7--books), our outer-space Indiana Jones; and Charley Pollard (8--audios), the self-proclaimed "Edwardian Adventuress." The remaining ones kind of grow into it. Mickey Smith (9-10) starts out a total wuss, but ends up crossing dimensions a few times to save the multiverse. Anji Kapoor (8--books) thinks of herself as rather ordinary but faces the things that terrify her with great courage.
RavenclawThe house the values intelligence and learning and is home to Luna Lovegood and Professor Flitwick. Above all is K-9 (4), the computer who loves to go for walkies. And then there's math geniuses Zoe Heriot (2) and Adric (4-5). Melanie Bush (6-7) is a computer programmer with total recall, and Liz Shaw (3) has a doctorate or two. Nyssa (5) is a bit of a brainiac, and the original Romana (4) likes to remind the Doctor that her grades were higher than his. Rounding out the category are three MD's. Martha Jones (10) displays quick reasoning, Grace Holloway (8) is intellectually curious (especially when it comes to guys with two hearts), and Harry Sullivan (4) is logical almost to a fault.
HufflepuffHufflepuffs are often called "a load of duffers" but often prove to be loyal and loving. These are the Dalek-huggers--literally, in Rose Tyler's (9-10) case. Other companions known for their compassionate, sympathetic natures are Jo Grant (3), who would make even the Master a nice cup of tea if she thought he looked a little down; Peri Brown (5-6), who, on her first trip in the TARDIS, pleaded with the Doctor to end one of the bad guy's sufferings; and Sam Jones (8--books), who cared so much for the underprivileged she got on a lot of readers' nerves. Fitz Kreiner (8--books) is a bit of a duffer, but he is nonetheless loyal. If the Doctor needs him, Fitz pulls through--though usually not without needing to change his shorts.
SlytherinThough most Slytherins can at worst be called self-interested, this is the house that has produced the majority of the evil or bigoted characters in the Potterverse. Believe it or not, the Doctor has traveled with a few would-be Slytherins. Adam Mitchell (9) tried to use his brief time in the TARDIS to make money. Turlough (5) at first only went with the Doctor to escape school, and tends to sneak off when danger approaches. Compassion (8--books) never really wanted to travel with the Doctor anyway, and once she got the hang of being a TARDIS, she dumps him off on Earth. Trix McMillan (8--books) also seems to travel with the Doctor for lack of a better option, and her selfishness often gets her into trouble.
Finally, there's Kamelion (5), who would not be in any house because, it, had it lived in the Potterverse, would be a Squibb.
So, a few discussion questions. (Yes, I'm gearing up for the fall semester. How can you tell?) What Hogwarts houses would the characters from your favorite fandoms belong to? What kinds of crazy crossovers would make your day?
*The Doctor and Rose made a cameo appearance in the Buffy Season 8 comics, so anything is possible. Which gives me hope for my crack theory about the 10th Doctor's regeneration involving a fob-watch and Dementors.