Today, with the release of Firefox 43, almost a decade after the idea was first mooted, there is finally an official 64-bit build of Firefox for Windows. To download it, you'll have to head over to the Firefox website and explicitly grab a 64-bit installer; if you just do an in-place upgrade you'll just get the normal 32-bit flavour.
64-bit Firefox for Windows is mostly identical to 32-bit Firefox for Windows, except that very few plug-ins will work with 64-bit Firefox. This is by design: Mozilla is in the process of dropping Firefox's support for NPAPI plug-ins. NPAPI support is being dropped due to (ostensible) stability and security concerns. Amusingly (or ironically), though, 64-bit Firefox does still support one plug-in: Flash. Sites that use other NPAPI plug-ins, such as Silverlight or Java, are being told by Mozilla to "accelerate their transition to Web technologies."
Over the years there have been a number of unofficial and alpha/beta builds of 64-bit Firefox for Windows, but they've always been aborted before they made it to the stable release channel. Back in 2012, an executive decision was made to halt 64-bit builds entirely due to "significant negative feedback" and a frustrating user and tester experience—but a few months later, that decision was reversed and the 64-bit builds continued, albeit very quietly.