Hillary Clinton uses Google Analytics
John Edwards uses Google Analytics
Barack Obama uses Google Analytics
Rudy Giuliani uses Google Analytics
Mitt Romney uses Omniture
We use Google Analytics for SoloSEO but I have heard Omniture is a great solution too. Setting up with Omniture takes a little bit of work because you need to put in variables for each page (like page name), but other than that it is pretty easy and has lots of features.
I would suggest the candidates use Crazy Egg and track where people are clicking around on the site. We’ve discovered a lot of interesting behavior on our site, I can only imagine having that much more traffic and learning what you can do to maximize it.