If I'm not wrong, all 64bit O/S can support 32bit programs. So technically all programmes that work as 32bits can work on 64bit. The only problem with Windows 7 is that they are different at core with XP, but if you're carrying over programs that you use on Vista, you're good to go even if they are 32bit. Correct me if I'm wrong, I'm not a IT expert.
You will only get any advantage out of using the 64bit OS if you have 4Gb or more of RAM. The 32bit OS can't effectively use more than approx 3.5Gb of RAM - the 'addressing limit' is 4Gb, but the application can't use all that, Windows needs a bit for it self. By going 64bit, the application/OS can make better use of the >4Gb RAM.
If you have less than 4Gb of RAM, using Win 64 is possibly even slowing you down.
In theory any 32bit application should work on the 64bit OS as it has a complete 32bit compatibility layer - but again if all your apps are 32bit, you are just adding overhead.
The problems with 64bit windows have more been related to driver issues, not applications - many bits of hardware still don't have 64bit drivers.
There are probably very few applications 'out there' compiled for Win64. One of the guys at work wanted to try his CAD program on 64bit (his models were getting too large and won't fit in the 32bit memory space), only to find the CAD vendor wants more money to 'upgrade' our licence to 64bit. The guys using Matlab are moving to it, as our licence is 'all platforms', but the heavy users are mostly running Matlab on 64bit Ubuntu Linux, not Windows.
It's our CAD guys who don't have the Linux option who are itching for 64bit.