Originally Posted by LondonElite

You will have a passport check in ZRH but not see your bags until you get to Rome. You will have no interaction with customs anywhere, unless you are importing goods beyond your allowances. If you do check bags these will go to Rome, unless you ask for them to be short checked to Zurich, which the agent may or may not be willing to do. If you decide not to travel to Rome, it is probably easier to call United to change the ticket to Zurich only.