The act of disabling JavaScript/Flash/Java should stop the font check, since those are the primary methods. This can be done in any major browser. I use the Firefox NoScript addon, which allows me to selectively enable JavaScript I wish to allow to run on sites, or specify some sites as trusted. It also blocks embedded objects, such as Flash and Java, until explicitly allowed.
My results on the referenced site:
+-----------------------------+----------------------------------+------------------------------------+---------------+
| Browser Characteristic | bits of identifying information | one in x browsers have this value | value |
+-----------------------------+----------------------------------+------------------------------------+---------------+
| User Agent | 9.89 | 946.25 | <too long> |
| HTTP_ACCEPT Headers | 13.71 | 13418.95 | <too long> |
| Browser Plugin Details | 1.91 | 3.76 | no javascript |
| Time Zone | 1.9 | 3.74 | no javascript |
| Screen Size and Color Depth | 1.9 | 3.74 | no javascript |
| System Fonts | 1.91 | 3.75 | no javascript |
| Are Cookies Enabled? | 0.38 | 1.31 | Yes |
| Limited supercookie test | 1.9 | 3.74 | no javascript |
+-----------------------------+----------------------------------+------------------------------------+---------------+
Thanks, Bob, but I don't really want to suffer the consequences of turning off javascript. I would prefer to "stealth" the piece of info that makes me 1 in 2,037,948 -- the installed fonts list. – mrblint – 2012-02-26T16:34:39.803