Obviously, a 64-bit processor has a 64-bit address space, so you have more than 4 GB of RAM at your disposal. Does compiling the same program as 64-bit and running on a 64-bit CPU have any other advantages that might actually benefit programs that aren't enormous memory hogs?
I'm asking about CPUs in general, and Intel-compatible CPUs in particular.
There's a great article on Wikipedia about the differences and benefits of 64bit Intel/AMD cpus over their 32 bit versions. It should have all the information you need.
Some on the key differences are: