Firefox 3.6 is actually still supported with security fixes, etc but for how long no one knows (I don't think it has been decided yet). I use a couple of add-ons that have not been brought into the newest versions and I have found issues with the newer versions on certain websites which aren't in 3.6.
I am employed working on software which uses web browsers as a front end. The short release cycle is a real problem for my company - we now have a team pretty much dedicated to fixing issues that appear in each new browser version (be it Chrome or Firefox, IE or Safari). It means I have everything installed... As I've found out, you can install both an old version of firefox (3.6) and the newest versions side by side - so long as you only run one of them at a time... Now if only the same piece of software would work the same on every operating system (Safari for windows behaves completely differently from Safari for Mac).