Do I need to add a new account for each new web site which I'd like to track?

The short answer is, "No". You may track up to 25 pages with one Invisible account and up to 250 pages with one Premium account. If you don't exceed these limits, you can track several sites with one account.

However, if you need to be able to assess the success of each individual site, you're likely best off creating an account for each individual site which you'd like to track.