Another option is to edit the field codes in Word to make sure all the leading zeroes appear. However, for a variety of reasons (such as a filtered spreadsheet or a conflict with a printer driver), this doesn’t always work. (See Mail Merge Problem: Leading Zeroes Missing from Zip Codes for instructions.)
The best solution to this problem is to change an option in Word that sets up a DDE connection with Excel, and displays the zip code the way it is formatted in Excel, with all leading zeroes.