Thanks in part to the lack of stability and plugin support, Mozilla's Engineering Manager Benjamin Smedberg has requested that developers stop building 64-bit versions of Firefox. If the idea of a 64-bit Firefox sounds strange, it's likely because it's not something Mozilla ever promoted. Instead, it was left up to the user to seek out a specific build on the FTP, which most of course never do. In all regards, the 64-bit version of Firefox was considered a tester's build.
To some, it seemed inevitable that Mozilla would officially release a 64-bit version at some point, but with this latest event, that time looks to be a long way off. With as few users as the 64-bit version must have had, plugin support hasn't been the greatest, and due to various development issues, Smedberg clearly wasn't interested in having an unstable 64-bit version continue.
For those who want a supported 64-bit browser, your options are limited. Windows 7 and 8 ships with a 64-bit Internet Explorer, although that's not likely to be picked up by many. Opera, since 12.00, has shipped a 64-bit edition (click "More options"). Chromium under Linux can also be compiled for a 64-bit architecture.
When 64-bit OSes first hit the scene, the uptake was slow thanks to similar things that Mozilla is mentioning here. Instabilities and incompatible software were common issues. It does seem probable that 64-bit browsers will become more of a need down the road, though, especially if we're expected to live life with our heads in the clouds.