All well behaving Windows application programs should work. The only exception being device drivers and all programs that access any device directly without using a device driver (this can only be programs for a specific type of hardware anyway and are thus actually device drivers). All device drivers are required to be 64 bit (even if they access 32 bit devices).
Any program that does behave properly isn't conforming to Windows specifications and is bound to fail on some computers anyway. Too many different hardware configurations exist and no program can cope with all of them (the device drivers solve these problems when the programs stick to the specs).
The biggest problem at the moment is that not all device drivers implement all the Windows specs properly. Over time that will be fixed for all current devices but likely several old devices will never get a (proper) device driver.
When switching to a 64 bit OS make sure that all devices are current and the last available device drivers are loaded also make sure that you power supply and cooling solution can handle the extra demands (even an idle 64 bit OS draws more that an active 32 bit OS). Provide plenty of RAM (minimum 4 GB, 8 GB preferred). And everything will behave just as good (and often even better). In those 32 bit program that need it you might actually get to use 4 GB.

Once the world gets used to 64 bit environments we may see all the benefits of this vast new space. Of course we will have to buy new computers (because 8 GB isn't enough anymore) but that keeps the economy going.