Well it is not that easy. Europe and Australia and Oz use GSM/TDMA cell phone network, while Verizon is CDMA.
For GSM systems you can just swap the SIM card and you are on your way, but your CDMA Sprint phone may not work on any GSM frequency in Germany.
On top of that, US cell phones are locked to be used only on the network of your provider, makes swaping SIM useless unless you first unlock your cellphone. It was possible to unlock/hack old cell phones, new smart cellphones communicate too much with the provider to let you get away with unlocking it.
I have a cheap and simple Samsung cell phone with a T mobile prepaid SIM card I use when travelling overseas, my US provider is AT&T, formerly Cingular, that´s actually GSM system with some minor differences in frequencies, but it will register and work in European cell phone network - it is very expensive in roaming charges, but it will work there.
Call your provider and ask them first, they can tell you based on your cell make/type what your options are. On EU airports you can find phone rental service or you can get cheap and unlocked cell phone on ebay before you go - make sure it charges in 220V grid - and buy prepaid SIM overseas.
