Open Options, go to Advanced panel and Updates tab, and select Never check for updates (not recommended: security risk).

Please note that Firefox 25.0.1 has security vulnerabilities and it's no longer safe to use.

Quite honestly, if don't like the newer versions of Firefox, just use a different browser - one that is up-to-date with security patches.

wildchild1954 said

I have an older version of Mozilla Firefox that I am quite happy with. Their new version caused me nothing but problems until I deleted it and reinstalled v25.0.1. Now all I get is constant barrages to update to the newest version. I want to know how to disable this update stuff so that I don't have to see this anymore. How can I disable the Mozilla updates?

the-edmeister said

Quite honestly, if don't like the newer versions of Firefox, just use a different browser - one that is up-to-date with security patches.

There isn't another browser out there that I like. And frankly there isn't a thing on the internet that doesn't have some kind of security problems. I've never had a problem with security using Firefox 25 so I'll just keep using it.