Firefox 3.6.8 does run on Windows XP. Here are the system requirements:

http://www.mozilla.com/en-US/firefox/system-requirements.html

Please make a backup of your profile before installing. See Backing up your information.

As for Firefox 4 beta, I have no idea.

Yes, Firefox 4 will run on Windows XP, but not on Windows 2000 (since Windows 2000 is now unsupported by Microsoft).

Also, do update to the latest version as soon as possible. The version of Firefox you are using at the moment has been discontinued and is no longer supported. On top of this, it has known unpatched bugs and security problems. I urge you to update to the latest version of Firefox, for maximum security, stability, performance and usability. You can get it for free, as always, at getfirefox.com.

The next beta should be working again on Windows 2000.

http://www.mozilla.com/en-US/firefox/4.0b2/releasenotes/
577486 – Check-in for Breakpad 64-bit on OS X dropped Windows 2000 support