According to Microsoft it's 2048. Since they invented the internet (and also the light, the darkness and Linux) they are right. :-) .... or.. and since IE forces this lower value, it's the lowest common denominator.
http://support.microsoft.com/kb/208427
Under Firefox, I see people on the net reporting URLs of 0xFFFF working:
http://forums.mozillazine.org/viewtopic.php?f=38&t=155648&start=0&st=0&sk=t&sd=a
Here is another post which talks about this:
http://hiox.org/index.php?id=425
EDIT: this is very sad that almost 5 years after I wrote this answer - it is still true. If you can, look at the history of this answer.
EDIT2: I found a better answer on StackOverflow - What is the maximum length of a URL in different browsers?
EDIT3: 9 years after - Explorer is deprecated in favor of Edge, Edge soon to be re-designed using Blink (making it very close to Chrome). I wonder how relevant this answer is.