Files will almost always be compatible. In the worst case, you can install the 32-bit software that created them on 64-bit Windows.
Drivers may not be available in 64-bit for old hardware, and may not be available in 32-bit for new hardware.
The only things almost guaranteed not to work on 64-bit Windows are 16-bit programs, which are no longer supported in 64-bit mode. However, you can probably run them in a VM, or DOS emulator.