Because I'm bored, and I had trouble with this not too long ago, I'll answer it to the best of my ability.
For most people, 32-bit is absolutely fine. The main difference between the two is in the instruction set, essentially the 64-bit feeds exponentially more complicated instructions to the processor. The main benefits for most people are faster processing times for 64-bit programs and the ability to map a lot more memory. 32-bit windows can only map about 3-3.5gb of memory if I recall, wheras 64 goes up exponentially to the point where we won't hit a limit unless we start using 50gb sticks or some such thing. I don't remember the exact number, the point is that it's way up there.
There are drawbacks to 64-bit. People claim it to be less stable, I don't know about that one for sure or not. Programs set up for 32-bit will most often run, but may actually run a little slower because of how the OS emulates a 32-bit environment. 32-bit programs will not run at all from a command prompt. Hardware also has to have 64-bit compatible drivers, so older hardware that is not plug and play might be a problem depending on what kind of legacy support the manufacturer operates. The good news is printers seem to get generic driver support through vista even if they don't have a driver but I believe HP and dell have updated for all their major ones. Scanners and game controllers are the most likely culprits. This can also cause a problem if a 32-bit program has embedded drivers.
Generally the only needs for 64-bit are high end gaming, CAD, video editing, etc. Those things get a considerable boost from 64 bit but until the industry gives it a wider acceptance (which it will eventually), 32 bit is still the norm and should probably still be the priority for 90% of people and their day to day operations. One alternative is to keep a 64 and 32 bit OS on dual boot so you can use one primarily and the other when you need it.