Internet Explorer has a 64-bit version and Chrome had its bits doubled in v37 (though it's an opt-in feature, despite being declared stable). Firefox has 64-bit builds available, but for the average user, they might as well not exist. That looks like it'll be changing next year, with Mozilla getting serious about promoting the browser's mainstream executable to the wider version.
A few years back it seemed Firefox 64-bit wasn't long for the world, yet development found a way to continue. Now it's very close to being ready for regular users, with the remaining work required being testing, add-on compatibility and cooking up an installer.
gHack's Martin Brinkmann noticed that the win64 page on the Mozilla Wiki received some attention recently, not only listing the arguments for upgrading to 64-bit, but the steps needed to get there. The first "phase", which will involve distributing an installer and an opt-in feature, won't take place until late March 2015.
At least there's movement and once Firefox is onboard, there will be virtually no limit to the abuse browsers will be able to dispense on your RAM.