LinkedIn used two initial phone screens (one with a recruiter, one with a hiring manager), followed by a day of interviews on site. I met with 7 different people on several different functional areas: research, development, and marketing.
Interviews consisted of a mixture of several things: questions about my background and experience, case studies, and technical questions. Interviewers asked specific questions about LinkedIn's products, and asked for ideas on how to design and build these systems.
I have never had as much fun interviewing with a company as I had with LinkedIn. I had a number of very intellectually interesting discussions. I also found that LinkedIn engineers were very friendly and outgoing; I got the sense that the goal of the interviews was as much to see if they wanted to work with you as it was to see if you could contribute technically.
If you are interviewing with LinkedIn, you'll find it helpful to learn something about LinkedIn's products. You should definitely spend some time using different features on the LinkedIn web site (suggestions, groups, messages), and should also do some research on the company itself (magazine articles, open source software projects, etc).