Can I have 64bit Linux installed on my Desktop PC?

Absolutely. This has been the default for a while, and the majority of linux PCs is 64bit already.

All it requires is a reasonably new PC (purchased summer 2004 or later). Where reasonably new means your PC is at least a Dell Precision 370 ("satyr", first purchased in Summer 2004) or a later model (Precision 380 "satyr", Precision 390 "oreade", Precision T3400 "pepe", Precision 3500 "Nomos", ...).

Actually, it's a valid reason to have your PC replaced by a contemporary model if it cannot run 64bit operating systems.

The 32bit variant is still available on request, but this will change with SL6. The 32bit setup receives little testing these days.