I've used LinkedIn for many years now, long before I joined Facebook ... I liked the concept of never losing contact information with business contacts and technologist. It just seemed like a good idea (though I do sometimes wonder if LinkedIn has any particular purpose).
I tend to only connect with people I've met in person, or at least talked to on the phone.
One thing that drives me crazy about LinkedIn is that when requesting a connection, you aren't forced to customize the greeting message from the default "I'd like to add you to my professional network."
As far as I'm concerned, this default greeting is like no greeting at all, and it's a sign that you are just trolling for contacts. Just like you should always write a cover letter for a resume, you should always customize this greeting message.
Your chances of successfully making a connection go up significantly if you do customize the message ... and with me, if you don't, your chances drop to near zero.