Check here, you'll need to click the hardware tab: Windows 7 Compatibility: Software Programs & Hardware Devices: Find Updates, Drivers, & Downloads
There isn't much in the way of newer applications that won't run under Windows 7 x64.
One thing to watch for if you do decide to install the 64-bit version (and I think you should) is this:
Under All Programs you will find a Program Files folder and a Program Files (x86) folder.
The former is the container for any 64-bit applications on your computer, whilst the latter is the container for 32-bit applications.
Also, if you use Internet Explorer as your default browser you'll find you have the choice of using a 32-bit version and a 64-bit version.
If you use the 64-bit version you need to be aware that Adobe have not yet released a fully-tested version of Adobe Flash x64 so some websites will lose functionality. However, Adobe have released a Beta version of Flash x64 so you could use that.
Stonebear's comment referring to RAM on a 32-bit system is correct.