I've been on LinkedIn for almost five years (you can find this information on your Account & Settings tab). Over the years, I noticed that once in a while when I clicked over to the person behind a connection request, they'd have recently connected to dozens of people. Shortly thereafter, that person would announce that they'd taken on a new role at a new company.
As social media has proliferated, I see more people getting involved to support their company brands - or just building their own. (THE resource on how to do this effectively is Dan Schwabel's Me 2.0.) These days it's not just LinkedIn connections, but new blogs, Twitter accounts, and ramped up public speaking appearances.
Don't get me wrong - there's nothing negative at all about this. In today's world of work, we all need a strong safety net and social media channels provide raw material, with a different thread gauges. But you should know that weaving a solid net takes time - and you need to start before you really need it. (For lessons on how to do this, here's some thoughts I shared last December on Warren Sukernek's successful job search.)
Also be aware that people are watching. And it's not just your potential future employers and colleagues, it's your current and past employers and colleagues as well. This is public, after all. So you may not need the old routine about a lot of sudden doctor's appointments anymore, but your boss might know what's going on anyway just by the digital breadcrumb trail of posts and tweets that you're leaving behind.
Better start weaving before you need to go fishing.