Professor Trelawney doesn't have a thread of her own! Hasn't the poor woman suffered enough? Then, I guess I'll take it upon myself to make a thread for her myself. I start it out with a question I have just started pondering on.
What house do you think Professor Trelawney was in during her days at Hogwarts?
I propose that whenever the question is asked: "What House did ____ belong in?", the arguments for (or against) each should be presented. Since we really don't know canonically where a lot of characters belonged, it's impossible to say for certain what the "right" answer is.
So, let's consider Trelawny:
Gryffindor: She was there at the Battle of Hogwarts, lobbing crystal balls at Death Eaters and werewolves! That takes some guts. And she knew people mocked her, but didn't seem to let it bother her. So she definitely has courage. And she really likes attention and respect; being a bit vainglorious is (IMO) a common Gryffindor trait as well.
Ravenclaw: I have a harder time seeing this. Her version of "divination" didn't seem particularly studied or organized. She made students use random methods any Muggle could think of based on pop culture, and made up her own interpretations. There's no evidence she actually studied divination seriously -- she just thought she should be able to see the future because she was a Seer, and when her "inner eye" didn't work, she convinced herself it did. I don't know if she was stupid or smart, but she certainly wasn't intellectually dedicated.
Hufflepuff: She doesn't particularly strike me as a Hufflepuff, but she doesn't seem not Hufflepuff either. I could see her fitting in there when she was younger. Perhaps it was her desire to get along with people and be liked that made her pursue her career as a Seer, even after it became apparent her gift just wasn't there (or rather, as we now know, it was, it just worked very, very infrequently). And for all her faults, Trelawney does seem to care about her students (albeit uttering dire predictions of death for one of them every year is an odd way to show it). I think at heart she's a good, if somewhat embittered and screwed-up, person, so she might have originally been a 'Puff.
Slytherin: Well, she wanted acclaim, as mentioned previously, and she saw herself as a great Seer. There's some ambition apparent there. (Though spending her entire adult life teaching Hogwarts' least-highly-regarded class isn't all that ambitious, when you think about it.) She also had no qualms about making things up to convince people she had more ability than she did. And even using crystal balls as weapons is kind of cunning. I could see her as a young Slytherin, wanting to prove herself and impress her classmates, declaring that she is the granddaughter of a great Seer and has the gift herself. And then she starts making up prophecies, and gets in the habit even after she's an adult.
So, my Sorting, in order from most to least likely: