They have set up a website to gather more data and give you a 'uniqueness' indicator for your browser, which you can find here. This data set is growing quite rapidly and will tell you how many of the userAgent strings they have received that are the same as yours. I managed to find a machine to test that was unique amongst the 195,000 machines they have tested. This means that someone could potentially track that machine even if cookies are disabled. Even if you come out with the same userAgent string as others, you can be narrowed down by using geolocation of your IP, browser plugins, installed fonts, screen resolution, etc. This isn't a new idea and others have tried it, like browserrecon. Of course if you have a static IP address then you are fairly easy to track anyway.
Various suggestions are made to help protect yourself, such as don't allow scripts to run on untrusted websites, which is fairly obvious. However, although this may reduce the amount of data given out from highs of 15.5 bits on a Blackberry or 15.3 bits on Debian, this won't stop the whole problem. It seems like the worst devices for giving out identifying information are Blackberry and Android phones, with minimum figures of over 12 bits. The best combination would seem to be FireFox running on Windows, which can be controlled down to only 4.6 bits (although highs are around double this), but this could just be because it's the most common combination.
What can you do? Don't visit untrusted sites. Also, you could change your userAgent string. It is just a text string stating the capabilities of your machine so that the web server can customise content to suit you. However, there is no real harm in tweaking this to fall in line with more common strings so that you are harder to track. You have to be careful here, because just removing most of the information will probably make your userAgent string unique. Alternatively, you could regularly change the string. Perhaps browsers should change the string with every connection? Plugins could do this, like User Agent Switcher. This would allow you to use different strings across different sites. Maybe hiding certain activities by temporarily switching the userAgent string would be useful.
FireFox and Opera are both quite easy to configure - type about:config or opera:config in the address bar respectively and navigate to the userAgent options. Internet Explorer is slightly more trickey, in that you have to make a registry change to alter the userAgent string. Navigate to [HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Internet Settings\5.0\User Agent] in regedit. Here you can create string values for 'Compatible', 'Version' and 'Platform' to control what is sent. Under the 'Post Platform' key are a whole bunch of additional parameters that will be added to the string, so you can change or remove these.