The 32-bit edition can only use up to 2GB of virtual address space on 32-bit editions of Windows (3GB if the OS is booted with the /3GB switch but it's not recommended), or 4GB on 64-bit editions of Windows. SQL Server supports the 'address windowing extensions' feature which allows more physical memory to be used, but it's not particularly efficient. The 64-bit editions (there are separate editions for AMD/Intel 'x64' processors - all new Athlon 64, Opteron, Core 2 and Xeon processors are - and Intel Itanium processors) can use a huge virtual address space - 48 bits' worth. In general, if you've got a 64-bit computer with the 64-bit OS, you should install the appropriate 64-bit version of SQL Server. If you have an Itanium system, you'd know about it and you wouldn't be asking the question!
Stability. What an interesting concept. -- Chris Maunder