Explain me about x64 systems?

My computer uses Wolfdale processor runs at 2.60 GHz. Level 2 Cache 2 MB. FSB 800 MHz. I know that this processor supports 64 Bit Architecture. I want to use 64 Bit system such as Windows XP 64 Bit Edition, Windows 7 64 Bit Edition. But some of my friends told me that if I want to use 64 Bit system, I must install the 64 Bit version of both OS and Application Software in order to get benefits from 64 bit Architecture. Can I use 32 Bit Applications in 64 Bit OS? For example, 64 Bit Version of Windows 7 with 32 Bit version of Microsoft Office 2007 Enterprise Edition.