I've noticed Firefox consumes significantly more memory whilst I'm watching Youtube Vids, but It doesn't seem to have a major impact on the rest of my system. Might be plugin-related? I had a similar issue with FF's Skype Plugin on other sites.
Good point worth noting.
The specs,
OS: Win 7
Browser: Fire Fox 3 <-> 4 (it persists on both versions)
Plugins: Adobe Acrobat, QuickTime Plug-in, Shockwave Flash
Extensions: Adblock Plus, Answers, AVG Safe Search, Flashblock, Greasemonkey, Java Console, NoScript, Skype Extension, UnMHT
Worth pointing out is that these issues have persisted for me longer than most of these plugins/extensions have been in use.
I've never had this issue, but...
First guess is, it's something relating to Macromedia Flashplayer. Is it possible to duplicate the effect using another site with large-ish flash videos? If not, what about youtube videos embedded into another domain?
Second guess, it's something to do with the advertisements that now blanket Youtube interacting poorly with something else on your computer. Again, trying to view youtube videos embedded in other sites would give useful information on this.
Additional note: I've been using IE8; dunno what you have.
This effect does not occur with anything that uses Macromedia Flashplayer. It is very specifically Youtube videos and how they work, in my testing experience. Embedded youtube videos produce the same effect on other websites.
I don't think the advertisements is a possibility, due to what I mention above. It's a possibility, since I have many advertisement and advertisement flash/java killing add ons.