Here’s my rule for connecting on LinkedIn. It works really well for me, so perhaps it might work for you.
I only connect with people that I have met physically or with whom I have some kind of substantial if physically remote connection. That means everyone in my LinkedIn network is somebody I actually know, not just another name on a list. And if I know them, that means they probably remember who I am… hopefully.
My rule also means that when I receive connection requests from folks I haven’t met, there’s a good excuse to suggest a face to face, which means I get to do two things I love. (1) Meet somebody new with whom to talk business. (2) Drink cappuccino in a cafe and call it work.
As far as I’m concerned, the purpose of a network is to connect people I know with other people I know to the benefit of both. Sometimes, one of those people might be me, but the power of a network lies in the ability of the person at its core to act as a useful intermediary. Where possible, I’d prefer to do this face to face, but where that’s not possible, in my experience there’s no better tool to use than LinkedIn.
The strap line for our legal practice, Particular C&L is “finding ways to get stuff done”. Competing for sheer numbers of “friends” is for teenagers.