Can you use the Nexus 4 without a SIM card?
Yes - all android devices will work without a SIM card, and can be connected to wifi for an internet connection.

EDIT: Just so people know, there is a setting in the build.prop file that determines whether or the not the device can be used without a SIM or not.

Most of the time this is set to allow it, however in rare cases it may be disallowed.