With a 64 bit x86 chip, you can run two versions of Windows:

Windows 32 bit versions, the normal XP/2000 and such that we have now. This runs 32 bit and 16 bit code fine, just as it does on a non 64 bit chip.

Windows x64 bit (the x64 is how Microsoft is keeping the terms seperate from their Itanium versions) will run on AMD Athlon 64 or Intel Pentium 4 with EM64T instructions. This runs 32 and 64 bit programs, but support for 16 bit programs is dropped.

So gaming wise, you could still play everything you do today on a 64 bit chip with the normal install of Windows. With the x64 one, games from 1998 and before might be showing signs of having 16 bit code and may not run. Though to avoid this, you could employ a dual boot between 2 versions of Windows.

The hard part about switching to Windows x64 today is driver support. All drivers it uses must be 64 bit.

With things moving towards 64 bit, my next wintendo will likely have a 64 bit capable chip in it. I'll just have to decide if I want a 64 bit OS now as well and deal with that possible hassle, or just keep the existing XP I use today.