Changing fingerprints won't save you
A lot of commenters here are saying that your browser fingerprint will change very often, as you upgrade plugins, etc. This is true, but it's not like how a digital hash changes completely when you change just one bit of the input data; the browser fingerprints only change slowly.
They cover this in depth in their paper:
From the abstract:
"By observing returning visitors, we estimate how rapidly browser fi ngerprints might change over time. In our sample, fingerprints changed quite rapidly, but even a simple heuristic was usually able to guess when a fingerprint was an "upgraded" version of a previously observed browser's fingerprint, with 99.1% of guesses correct and a false positive rate of only 0.86%."
And that, as they admit, is only using a very crude algorithm.
The best way to look at this is as a very power "super-cookie" -- like a Flash Cookie but much harder (currently) to defend against. This _is_ a big deal. It gives any website that you visit regularly the ability to know that you are the same visitor as earlier, even if you don't log in and don't accept cookies. And if you have ever identified yourself to that website in the past, they will know who you are even when you visit the site again but don't log in.
This technique must be a favourite of the spooks. And only the browser makers can really fix it -- an add-on that homogenises your fingerprint will only be as good as the number of people who use it, which will be a very small number indeed.