I have differing rules based on the platform. For LinkedIn I used to accept any invites (can't hurt to connect, right?) but started being more selective as time went on. Now I accept those that I know, have connections in common, or sometimes those who work where I used to work. I try to keep it to people who I know or those who may be able to help me later on. I've started de-connecting with some because they weren't people I would ever turn to. Some employers will also look at LinkedIn profiles to see who you know and what they say about you, so it's usually in your best interest (IMHO) to not be connected with every random person that requests it.
For Facebook I only friend people I know. At first I was hesitant about accepting family requests (I joined Facebook back when it was still for .edu email addresses only) because it just seemed like an odd intrusion. I got over it and accepted my dad's invite a week later
I did defriend one uncle because he was making really frustrating comments on my pictures and posts. He made fun of my dog, my wedding pictures, etc. I finally gave up and removed him, I don't need that kind of drama on my Facebook page. I use it to keep in touch with college friends, reconnect with some from high school, and see what coworkers/former coworkers are up to. Although the coworker thing can get tricky sometimes.
And same with Twitter- only people I really know. But I barely update there, so it doesn't matter as much!