Regardless of OEM or retail, it depends if you are getting and installing the 32-bit or 64-bit version.
64-bit version will run most 32-bit applications but it is not a 100% guarantee that ALL 32-bit apps will run. However, you will need 64-bit drivers for your hardware.
OEM versions come in either 32-bit or 64-bit, not both. Retail ones mainly com in 32-bit, with the exception of Ultimate, which comes prepackaged with both DVDs. For the other retail versions, you can request for a 64-bit edition from MS but I'm not sure about the process as I own the OEM edition. If someone could clarify the last part it would be great.