(I'm replying to this comment as a form of bookmarking, so I can find it later by searching my own comments. Upvoted, needless to say.)

Yes, they do. My company's web site allows signup through Facebook, and we get about a quarter of our (substantial) signup volume in that form. It's especially common in people who arrived on a mobile device; presumably it's easier to just tap "Sign up with Facebook" than to enter an email address and password by hand.

But I personally have never done it and don't expect to.

Facebook already snoops on your browsing habits, certainly on any page that offers it as as a login option.

I've signed up for a few things with my gmail account.

I do. I don't really care whether FB know about my browsing habits.

I can confirm that the couple of times Google sent me to Quora I left the site as as soon as they required my registration to read, not just post.

I've had the same reaction for the same reason. I might give it a second look after the favorable mention in this post, though.

Side note: do people really use "sign up with <...>" buttons? I can't imagine agreeing to let facebook snoop on my browsing habits outside their site, or let twitter tweet on my behalf.

In what way would you predict that allowing facebook to snoop your browsing habit will have an impact on your life?

There are two major forms of this, OpenID and OAuth. OpenID is only used for identification, while OAuth gives some form of limited access that is sometimes restricted enough that it's basically just used for identification. The permissions granted by using OAuth varies by site, but they usually show you what information they will be sharing before you accept.

There are benefits for both the developers running the site and for the end-user.

For example, BambooHR, the cloud-based HR software we use where I work, allows me to log in with gmail. Google is an OpenID authentication provider so no information is shared. Also, since I'm always logged into my gmail, it's just a single click to "log in with gmail" and I don't have to type any passwords or anything. (In fact, I never had to set up a password to begin with)

For more info on how OAuth and OpenID are different, there's a nice graphic here.

In case someone else is interested, I have been able to bypass most of the Quora annoyances with the Chrome Referer Control extension. Similar tricks exist for other browsers.

That probably used to be the case. But, now that AMAs are streamlined, subreddits are becoming more known, and killer modteams like askscience and askhistorians have developed, reddit is significantly more attractive to famous people, academics, etc. than Quora is.