ia64 = Intel Itanium
ia32 (formerly known as x86) = Intel P4, Intel Xeon, AMD AthlonXP, AMD Sempron
amd64 = AMD Athlon64, Athlon64FX, and AMD Opteron.
the current amd64 architecture CPUs are reverse-compatible to ia32.
Intel's next-gen processors will incorporate "EM64T" which is a set of 64-bit memory extensions. read about it
here .
It's interesting how history repeats itself...20 years ago, the Motorola MC68000's 32-bit extensions allowed it - an 8-bit CPU - to power the new Macintosh and Amiga platforms.
One might also draw comparisons between the ia32 -> amd64 and m68k -> PowerPC transitions.