Firefox's update notifications do not look like little messages in websites. Or big messages in websites. Those messages are from the sites themselves, reminding you that since older version browsers often are full of known security holes, they recommend updating, and also, they get weary of supporting so many different feature sets.

Is there some reason you're holding back? Obviously some work (i.e., configuring add-ons) is involved in retaining the old appearance of Firefox 28 in later versions, but forum volunteers have helped hundreds of users with that over the years.

Mozilla discloses security flaws after each new release, so... give it some thought.

@Jscher2000 I didn't like the way Firefox looked after 29.0, too much like Mac. Even with the add-ons to retain the 28. and earlier appearance, I perfered it the way it was. I have Aspergers, so change and I don't get along. So I have kept it as is since. But now I'm getting the "update your browser" messages on more and more sites.

https://addons.mozilla.org/firefox/addon/classicthemerestorer/

This Classic Theme Restorer extension was made for those who did not like the look of Firefox 29.0 and on. You do have to do a little tweaking in this CTR extension to make Firefox look the same or better even as Fx 28.0 as just installing the CTR extension is not enough.

Many sites may be using things that are only supported in the more recent versions so that is a reason for websites to try and get you to update.

Firefox 28.0 is pretty old now as it came out back on March 18, 2014. https://www.mozilla.org/firefox/releases/

Yeah, I stick with things for awhile. For example, my computer, it's from 2002. I still had a tube TV until two years ago. I'm not old either, only 35, just set in my ways. But I'm beginning to realize I'm gonna have to upgrade. Just wish there was another way.