As I recall, you can run Firefox from anywhere you want. I've run it from my home directory before. All you have to do is copy and paste shortcuts for your plugins. Works just fine.
Heck, you could probably even put it on a jump drive this way...in fact, I think I did that once, too.
With Linux, if you have multiple users on a box, they could all run their own copy of firefox very easily. Just untar the app to your home directory, then change the value of "moz_libdir" to "moz_libdir=~/firefox/firefox" in /usr/bin/firefox. This way, each user can run whatever version they want, and they can update it any time they want without having to have access to system files (i.e., root).