LinkedIn can be a powerful tool for use within part of the networking process, but is certainly not applicable to the entire process.
Seth Levine has written an extremely useful short series of blog posts about networking (links at end of post). In his Networking 101 post, one of the steps, step 2, is to "exercise your existing network", which involves tracking down people you'd like to meet through people you already know. LinkedIn is perfectly suited for this purpose.
Benedict Casnocha pointed out in one of the comments on Mr. Levine's blog entries that there are some parallels between Mr. Levine and Keith Ferrazzi's networking process. Mr. Ferrazzi may be the ultimate networker. Although Mr. Ferrazzi's style is much too over-the-top for me, I think he offers a lot of great ideas.
Seth Levine's Blog Posts
(Read the comments for valuable information):
Networking 101 Expanded
Here's how you do it
About Keith Ferrazzi:
Meet the MasterMinds: Connecting with Keith FerrazziThe 10 Secrets of a Master Networker
Never Eat Alone
Benedict Casnocha's home page