We know it's possible to look up the IP of a visitor using JSON and a callback, as seen here Can I perform a DNS lookup (hostname to IP address) using client-side Javascript? and also at http://news.ycombinator.com/item?id=1896015 - but what about a similar thing for the user agent?
This string is directly available in navigator.userAgent. However, this string is not very reliable, because the user can easily modify it. Only use it for non-critical purposes.
If you want to detect the user agent, so that you "know" what's supported, you'd better switch to capability-detection.
Examples of alternative methods to detect the browser:
IE: Conditional comments (HTML (also includes IE version) or in JScript
Firefox / Webkit / Opera: Setting a CSS property with a vendor-prefix, and checking for the existence of the just-set property.