TrendIQ has been measuring changes in the "internet presence" of the Social Networking Sites on the internet since February 8, 2004. Social Networking sites are an emerging human networking technology utilizing the internet to build personal networks. Trend-IQ: Social Networking Information
If you follow the link, you can see the graphs and easily compare how popular different sites are.
LinkedIn is really exploding, so much so that there is a second graph with the LinkedIn data removed so that you can more easily see the variation among the other services. Anecdotally, this has been my experience as well. And, although I had my doubts about it initially (there is still nothing to "do" there), its business opportunities seem to contain enough potential for it to be useful.
The way I use LinkedIn is to make my first email contact with someone via the service. I'll copy business card information into my address book, then export the information to vCards. These vCards can now be imported into LinkedIn, and I can then send invite messages to these people.
This invite message usually takes the form of reminding people where we met, any information we talked about exchanging, then an intro to the service. Since the messages are sent with my email address in the "From" field, people can easily hit "Reply" and respond as normal, as well as checking out the links to the LinkedIn.
The "hit rate" of how many people actually sign into LinkedIn seems to vary widely. A better strategy might be to send an introductory email mentioning LinkedIn, and then an invite with a very short message (so the LinkedIn URLs are more clearly highlighted). Since I have been sending out quite a lot of invitations lately, I'm going to do some follow-up work to see why people haven't checked out the service.