One thing to keep in mind is that many pieces of software use mathematical approximations in their code to allow for faster execution and easier compilation into assembly, without losing needed precision or functionality. For example, in a game a rotation may be represented by the multiplication of some sine and cosine functions. It is more efficient to represent a large rotation as a sum of many small rotations (which can ususally be done in a minimal number of clock cycles) as oppossed to larger rotations. Even if the code is ported to 64-bit, there may not be a reduction in clock cycles needed to solve the equation. As a result, you may not see much of a performance increase from 32-bit to 64-bit (x86_64).
Scientific applications or anything where you have large sets of larger numbers, you would definitely see an improvement in speed. Games probably not as much as you would expect.