How are your applications running? Are they experiencing performance problems? Are you looking to scale upwards to a larger system or possibly run more applications on that server? If everything is functioning normally, then I wouldn't try fixing something that isn't broken. If the hardware and, possibly software, versions are about to go to expire, then it may be time to move on.
The fundamental question here is: does your application support running on 64-bit hardware and a 64-bit version of the operating systems kernel that you would be using? It is not a trivial undertaking to port software from 32-bit code to 64-bit code. You'll need to contact your vendor and find out these answers. You will also need to confirm that all applications running on the box are supported on a 64-bit kernel. Why would you want to move to 64-bit hardware and use a 32-bit kernel? If you are using a host monitoring tool like BMC Patrol, or backup software like Tivoli, you will need versions of software that support a 64-bit kernel.
Regarding best practices, I would create some kind of sandbox environment to perform all your testing in. Assuming all your applications have fully supported 64-bit code versions, find an appropriate hardware platform for your testing and get to work. There are no short-cuts for this type of work. You do NOT want to be touching your live systems, prior to you completing a Proof of Concept (POC) for the 64-bit migration.
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