To disable favicons in Firefox, open the browser and type about:config into the URL bar, then press Return. You may then see a warning about how modifying advanced settings may void your warranty; click the "I'll be careful, I promise" button to proceed anyway. You'll now be looking at a long list of preferences, along with their status, type, and value. In the Filter box above the list, type browser.chrome; this will greatly shorten the list of preferences.
In the resulting list, double-click on browser.chrome.favicons to change its value from true to false. Then double-click on browser.chrome.site_icons, to set that preference to false, too. That's it; you're done. From now on, you'll no longer see favicons as you surf the net.
To reset things to normal, just reverse the process--go back into about:config and double-click the same two preferences again to set them back to true.
For Safari, first quit the browser, then open Terminal (in Applications -> Utilities), and type this command:
defaults write.com.apple.Safari WebIconDatabaseEnabled -bool NO