I use LinkedIn as an online social (well, professional) networking tool. It works quite well for me. I’ve come across a lot of interesting opportunities through it.
People who’ve worked at the same company as I have, during the same time period I worked there, try to link with me. This is great when I’ve actually interacted with them. Sometimes, people I’ve never heard of try to contact me… when you work at a company with 70,000 employees, there’s a slight chance that you haven’t heard of most of them. The first couple of times this happened, I accepted the invitations, only to break the links later. The next few times, I send a polite question back along the lines of, “My recollection of my time at BigCo is a bit hazy, can you remind me what project we worked on together.” No one ever answered back, until today. The reply was, that we’d never worked on a project together, but that he’d be a good contact.
What should I do with these invitations? Explicitly decline them? Let them expire? I generally feel that I shouldn’t accept them. My baseline criteria for sending or accepting an invitation is, “Would I be comfortable telling this person about a job opportunity if I bumped into them face-to-face.” Since I’m an introvert, I generally wouldn’t feel comfortable going up to a stranger and talking to them. I’d also feel somewhat uncomfortable if a stranger came up and talked to me.

FWIW, I get lots of these, having worked at five large companies. I generally just let them expire. I do, however, add every single person I work with at my current company, just in case they end up adding lots of contacts later.