The first 64 bit computer I used for CAE work was a Cray X-MP back in the mid 80’s.  At that time, the IBM PC was an 8 bit system, and wasn’t used for much CAE work at all.  A few years later the IBM AT came out, and it was a full 16 bit system, and while that was a big improvement, almost all CAE work was still done on specialized workstations, mainframes, and supercomputers that had higher speeds and memory capacity. That Cray X-MP had a huge storage capacity for the time of 32 Mb of RAM, but that’s less than an iPhone has today.

Once Windows moved up to 32 bit hardware and operating systems, it became more common to use CAE applications on Windows, and more so when Windows XP was released in 2001 using some of the NT technology.  I starting using Windows XP x64 around 2006, and I’ve been using 64 bit windows versions ever since.  The big advantage of 64 bit systems is that you can access more memory.  A 32 bit OS has a 4 GB address space, but the Windows OS and other hardware like graphics cards use up some of that space, typically leaving only 2.5-3.2 GB total free memory for all applications.  Modern CAE applications like NX, FEMAP, and NX NASTRAN often need significantly more than that to run some models, and even the standard office applications can use up much of the available memory on a 32 bit system if you run several applications at once.  A 64 bit system can theoretically access 16 Exabytes of memory, although current operating system and hardware limits are much less.
If you are still using a 32 Bit operating system running CAE applications, I would highly recommend that you upgrade your operating system soon.   NX 9.0 and NX NASTRAN 9.0 only come in 64 bit versions.  Femap 11.1 is the last version that will support 32 bit, and the 32 Bit version of Femap 11.1 comes with NX NASTRAN 8.5, since that is the last version of NX NASTRAN that supports 32 bit.  A 32 bit operating system is just too restrictive on memory for modern CAE model sizes.
If you are wondering how much memory your 64 bit Windows operating system can handle, the current software limits are 192 GB for Windows 7 Professional, Enterprise, and Ultimate, and 512 GB for Windows 8 Professional and Enterprise and 128 GB for the base Windows 8.  Those are the OS limits.  There are hardware limits in each system that typically are lower than the OS limits for the entry level machines.   If you are thinking that 512 GB may not be enough RAM, then you can use Windows Server 2012 Standard or Datacenter, which has a 4 TB limit.  And I still remember the 640K limit of the first IBM PC and that 32 Mb Cray X-MP.  Today, we have customers running 32 GB and more on CAD/CAM/CAE desktop machines to improve performance.