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 you aren't forced to customize the message. As far as I'm concerned, the default message is like no message at all, and its a sign that you are just trolling for contacts. Just like you should always write a cover letter for a resume.
So the first rule of LinkedIn is: always customize the message. You chances of a connection go up significantly (at least with me) ... and with the default message, your chances drop down to near zero.