If you had a reason, Mozilla has been compiling Firefox Nightly as a 64-bit application for Windows over the last several months. It is not a build that is designed for the general public; in fact, I believe it is basically only available to make sure that they did not horribly break anything during some arbitrary commit. That might change relatively soon, though.
According to Mozilla's "internal", albeit completely public wiki, the non-profit organization is currently planning to release an official, 64-bit version of Firefox 37. Of course, all targets in Firefox are flexible and, ultimately, it is only done when it is done. If everything goes to schedule, that should be March 31st.
The main advantage is for high-performance applications (although there are some arguments for security, too). One example is if you open numerous tabs, to get Firefox's memory usage up, then attempt to load a Web applications like BananaBread. Last I tried, it will simply not load (unless you clean up memory usage somehow, like restarting the browser). It will run out of memory and just give up. You can see how this would be difficult for higher-end games, video editing utilities, and so forth. This will not be the case when 64-bit comes around.
If you are looking to develop a web app, be sure to check out the 64-bit Firefox Nightly builds. Unless plans change, it looks like you will have even more customers soon. This is unless, of course, you are targeting Mac OSX and Linux, which already have 64-bit binaries available. Also, why are you targeting specific operating systems with a website?