Although 64-bit computing is gaining in popularity, a frustrating amount of applications still only utilise 32-bit builds. Yes you can run them on a 64-bit machine, you don't get any of the performance benefits. One of the obvious benefit of running a 64-bit version of Windows is that it enables you to access more than 3a larger amount of RAM, speeding up your machine.
For those who use Firefox and and want to benefit from your 64-bit machine, take a look at Waterfox. This is a dedicated 64-bit browser based on Firefox’s open source code, compiled specifically for 64-bit versions of Windows, complete with a number optimisations and enhancements for improved speed.
Note that Waterfox shares your Firefox settings.