There are three things at work here:
1. Is the processor 64-bit? AKA: Is the processor capable of running 64-bit code. If you have any Intel-based system *OTHER* than the very earliest 2006 systems with a "Core Duo" (or Core Solo, which was an option on the Mac Mini,) then the processor is 64-bit. *EVERY* "Core 2 Duo", *EVERY* Xeon, and *EVERY* "Core iSomething" is 64-bit.
2. Is the Kernel 64-bit? This is significantly less important than you think. By default, only the Xserve would boot into the 64-bit kernel. Really, the only thing this affects is if the core of the OS can access more than 4 GB of memory for its own internal use. This has no bearing on applications running 64-bit code, or using more than 4 GB of RAM.
3. Is the application 64-bit? This is what matters to most users. If #1 is "Yes", and the application is capable of 64-bit operation, then you're good. For the most part, the only gain you get by running in 64-bit mode is that individual applications can access more than 4 GB of RAM. Standard consumer applications have effectively no reason to do so, only higher-end applications often need the use of that much memory. (Right now, any way.) Also, because of the way 64-bit mode works on Intel (and AMD) processors, *ALL* operations see a very slight performance increase running in 64-bit mode vs. 32-bit mode - if the application is capable of 64-bit mode. In general, this performance boost is under 10%, though, so for most uses, it's barely noticeable.