HypersomniacLive: Firefox is a known memory hog, but I never had such an experience (perhaps me not allowing every single site to run all sorts of javascripts has something to do with it), and I must say that the latest few versions of it behave quite nicely.
This is a common misunderstanding. Firefox is not a memory hog at all. The browser itself doesn't use much memory however modern web pages contain dozens if not hundreds of megabytes worth of content data, especially the graphics. The modern web is loaded with graphics and while a lot of that is heavily compressed JPGs that appear to be small file sizes on-disk, they have to be decompressed into memory for display on the video card, and they expand tremendously and consume much more memory than they do on disk. That's true of any browser or application that displays graphics. A very very long time ago back before Firefox 4.0 the browser had some memory leak problems and some other memory issues but those were stomped out a very long time ago now and the entire memory subsystem in the browser rewritten to be much more optimized.
The biggest issue with memory consumption outside of that is via plugins and extensions of which can allocate more or less as much memory as the author chooses too, and they can leak memory also. AdBlock Plus is the number one most common browser extension used in Firefox by millions of people, and it is known to leak a lot of memory also. Other extensions leak memory or use way more memory than they really need to, however all of these extensions once loaded are part of the Firefox process and so as they leak memory or use it, that memory shows up in the task manager as being Firefox memory steadily increasing. Firefox then gets blamed for being "bloated" which is nonsense.
Uninstall Adobe Flash, uninstall all extensions completely and reproduce any "bloated" issue with the base browser. It probably wont happen, because they took care of such issues in the core browser 5+ years ago.
When you are experiencing memory related issues with Firefox, go to "about:memory" in a spare browser tab, then click on the verbose setting and you'll get a highly detailed breakdown of all of the memory in use in the entire web browser. The majority of memory will be used by extensions/addons and by web page content, in particular javascript. The modern web has tonnes of poorly written javascript and it will abuse the memory of the browser whimsically knowing that the browser will get the blame for it instead of the crappy web developer.
For those experiencing problems due to memory leaking of AdBlock Plus, search for a new ad blocker that uses the same filter lists which is called "uBlock Origin". It is optimized to use a fraction of the memory and CPU resources compared to AdBlock Plus and I'd recommend that to anyone as an alternative. If you use any AdBlock Plus addons such as Element Hiding Helper or Popup Blocker though you'll lose them as similar replacements aren't available for uBlock Origin that I'm aware of. Memory use will go way down though as AdBlock Plus is a memory leaking hog.
I suspect that even these issues will be greatly reduced when Mozilla switches to the Electrolysis based Firefox over the next 18 months and support for XPCOM/XUL extensions is phased out, removing some of the freedom existing extension authors have to write shitty code and not care.