[mindcrime]

Usually, but with a few exceptions. If a random person tries to connect with me, and one (or more) of a few conditions is true, I almost always accept. Those conditions would be things like "We have a lot of connections in common already", "they include a note explaining why they want to connect", "it's apparent from their profile that we have common interests that justify connecting", etc.

OTOH, a few "red flags" almost always cause me to decline. Some of those are "the profile looks obviously fake" (these are the ones where the picture is a beautiful blonde woman, and her profile shows no education history, one job with a generic description like "retail" and they have like 5 total connections, and none in common), or "some guy in another part of the world, in a completely different industry, with no obvious sign why there would be any mutual interests, and there's no note explaining why he wants to connect", etc.

That said, if one of you sends me a connection request saying "Hey, this is 'soandso' from HN" then I would almost always accept that.

[chrisBob]

You get requests with a note explaining why they want to connect? I don't think I have ever seen anything other than the default message.

[mindcrime]

Not many, but every once in a while I'll get something like "Hey, I saw your article on X and really enjoyed it and thought we should connect" or something of that ilk.