I never really paid too much attention to it until recently.
On my main Windows 7 installation (a virtual machine on my iMac) with 16 GB of RAM assigned I checked the three browsers I have installed (Firefox, IE and Chrome). Each has Adblock Plus installed and home page set to Google.
I started Firefox and there was a single item listed in Task Manager taking 290K of RAM.
When I opened Chrome there were originally a dozen items listed in Task Manager then it dropped down to 6, with a total of 150K of RAM usage.
When I opened IE it showed 2 items with a total of about 135K of RAM.
I used to use Firefox almost exclusively, both on my Macs and Windows machines. I have started to use Chrome much more often recently though due to some serious issues with Firefox. For instance, it doesn't play nice with the FCC search pages and tends to get stupid after playing videos on Facebook, Youtube or Vimeo. Chrome and Safari have not had these issues. I almost never use IE so I couldn't tell you if it has these problems or not.