Sometimes they do also have address information, sometimes they don't. As with everything, it will reduce the amount a fraud a bit but not eliminate it.
ZIP codes seem to be a US-specific thing.
ZIP codes are just a funny name for post codes, and most places have postcodes.
While many places have postcodes, most don't have postcode validation for credit card transactions. And it wouldn't really help to combat fraud anyway.
Damn you Ireland and your "no postcodes" hell.
We have postcodes now! Or well, eircodes. Which are totally not postcodes, but rather unique house identifiers that happen to look as postcodes. And that noone will use.