Should I install 64-bit versions of operating systems?

Yes absolutely. I haven't encountered any hardware or program issues. All of your 32-bit applications should work fine. Mine have. Windows 7 has got to have the best hardware support Windows has ever had

The main advantage is of course more physical memory for the computer. The disadvantage is that applications tend to use slightly more memory due to the implementation of 64-bit architecture. Most people going 64-bit usually upgrade the amount of memory anyways so this isn't that big of a problem. If you don't multitask that much it shouldn't affect you either way. The majority of your 32-bit applications should work fine.

Some hardware, especially if its old, won't work on a 64 bit machine if you can't find drivers for it.

Two pieces of hardware I ran into problems with was my Treo and an older HP laser printer I had.