There is a known Trojan that crashes Firefox 6 but not earlier versions. It may be sensible to do a full security scan on your computer, if you try that please say what software and version you used ? (The malware still affects earlier versions, and indeed other browsers, but does not result in crashes)

If you have genuine Windows software, I understand MS provide free security software in most parts of the world.

Because many updates to Firefox are security related it is normally recommended you use the latest version, or downgrade to an earlier supported version, that would currently be Firefox 3.6

Have a look at firefox crashes are you able to get crash IDs for the crashes you are experiencing ?

If you crash on certain websites, it may not be surprising if tabs related to those websites (or open whilst having crashes) cause problems!

Clean installation of WinXP x64. No firewall, no antivirus, no any other software. Just started IE to download FF from mozilla.com directly after network driver installation. Problem is the same

sdvv
I suggest you start your own question and supply full information.

Also try Firefox in Firefox's safe mode, and with plugins disabled.

If you are using no firewall and no anti virus what is your policy? Do you have full backups and are prepared for bare-metal re-installs, as opposed to trying to cleanup after the inevitable malware problems.