Finding people

These two sites can be used to find people at a specific company and to find people you used to work with.

Linked In -- you have to register and link to someone else's network to get any value out of this site. Linked In is a professional network.  This is currently a free service.  I personally use Linked In because it seems faster than Zero Degrees, and seems to have more subscribers.

Zero Degrees -- This is a professional network, like Linked In. This network is modestly priced, and has a free two month trial period.

Finding people you used to work with

Eliyon -- This site will tell you where people you used to work with are now.  The free version will not tell you who is currently at the company you are interested in.  This is a good way to get in contact with, say, an ex-manager who will give you a good reference.  Note that the paid version will tell you who is working at a given company, but its quite expensive.
 

Yahoo People Search -- If you know where they live, you can find them.

Google -- Often you can find past associates by searching in google, or in the Usenet groups archive.

Other

Ryze -- This is as much a social network as a business network. You have to pay if you want the advanced search tools.

Plaxo --  An automated utility to keep your outlook and outlook express address book up to date.  I haven't used it because I don't use outlook, but a couple of my contacts have.

Job Search

A list of job search sites and hints has been added at Job Search Resources due to the number of requests.