Who knows when the tipping point was for browsers going from lightweight affairs to the memory-destroying pieces of software they are now. Besides throwing more hardware at the issue, you do have some options for figuring out where all your precious RAM is going, at least when it comes to Firefox.
Martin Brinkmann over at gHacks has put together a short guide on to step you through the diagnostic process. The first stop is starting Firefox in Safe Mode, which loads the browser without extensions. You can then peruse the internet as usual and observe the program's memory consumption.
If it's significantly less than when Firefox is in normal mode, Brinkmann recommends checking out your add-ons for bad behaviour. Funnily enough, it's an add-on that comes to the rescue here: Tab Data (+Memory Usage).
As the images above illustrate, Tab Data comes with a nice array of tools for figuring out Firefox's memory usage, down to each tab. It may take a little time to nail down which add-on is at fault, but eventually the culprit will reveal itself. With some luck, a less RAM-intensive alternative will be available.