Interesting. I feel that leaving it in points it out more than changing it does. Especially if I'm only quoting a sentence or two. I can see it being different if I'm quoting an entire post.
Me too, I've always thought it was more polite to fix the typos -- keeps from drawing other people's attention to it.
Whereas I see the "fixed it" post when you disagree with someone as being quite snarky/rude. Funny how opinions can differ so much.
I've really only noticed the "fixed it" thing when people were trying to be funny, for the most part. But no way would I ever correct someone's typo. That would just feel pretentious.
What would make it pretentious? I'm not arguing, just trying to understand this to decide whether or not I should stop doing it...to me it just seems like the nice thing to do, so I'd prefer to keep doing it if only a few people are bothered by it as the exception.
I usually fix typos in quotes because I assume if the poster had noticed it, they'd have fixed it themselves, and it can clear up confusion. Typos seem much more glaring in quoted posts. Particularly if I'm debating with someone, I don't want them to think I pulled out that post to deliberately emphasize their error! Better to correct it and pretend it wasn't there in the first place.
But if there's a real reason not to that someone can explain, then I'll try to remember to stop. 
By correcting it, you're drawing attention to the fact that is was wrong. People who just read the first one then read yours are likely to noticed you've corrected it. To me, that is double pointing out the error. It's like smelling a fart and pointing out that you're pretending to not smell it (under the polite fiction that the person didn't fart at all to begin with).
On top of that, it also kind of says, "Hey, you didn't do well enough in your original post, what with your typos, so I'm going to fix them for you and do a better job!" I know that's not the intent, but it still comes across that way, to me, anyway.
