There isn't anything a 64-bit program can do which a 32-bit program CAN'T do, with the sole exception of accessing more RAM. Most programs need a lot less than a couple GB of RAM, and so by themselves they don't need a 64-bit OS. The only exceptions are a few categories of applications such as video editors, batch processing of huge photos, large databases, etc.
But even if you only use 32-bit programs, if you run ENOUGH of them then collectively they can use up 4GB or more of RAM. In that case you're better off with a 64-bit operating system, because it will be able to keep all those programs in RAM without having to slow down to read them from disk as you switch between them.
The rule is: 4GB or more of RAM --> use 64-bit Windows (note that 32-bit Windows can't access the entire 4GB of RAM).
If you use 64-bit Windows, then don't worry if you can't find a 64-bit version of a particular program. In most cases the programs that actually need 64-bits have 64-bit versions available (Photoshop, for example). If there isn't a 64-bit version available, the program probably just doesn't need enough RAM to make a difference.