As Pepita said, GeoBase is really good at geocoding with ZIP codes!
Or do you mean that you'd like to draw ZIP codes on a map? Similar to the way that cities/states/countries are labelled -- with the ZIP code written on the map at the center of the ZIP code's location?
(1) Create a custom renderer; or (2) Use a custom map style.
I'd go with the custom map style. It sounds like the 'proper' way to get what you want :)
Either way, you'll have to use the Alchemy data import tool (included with your GeoBase install) to get your ZIP code data into GeoBase. Alchemy can read ShapeFile data (amongst other formats) so download your ZIP code data in ShapeFile format from the census website. Use Alchemy to create a custom table from your data, you'll want at least two columns in your table: something like ZipCode (eg "54474") and ZipPolygon (describing the bounds of the ZIP).
Next, you'll need to load the data into your GeoBase app. This is literally a one-liner, just create a new MultiRepository to manage your data and pass the MultiRepository constructor the path to the folder containing both your custom data and the map data you want to use.
If you're going the custom renderer route there's a tutorial you'll want to check out in the GeoBase Reference Documentation (packaged with your GeoBase install, or at http://docs.geobase.info/):
GeoBase | GeoBase Tutorials | Renderers
Otherwise, use the custom map style. This is probably the fastest way to get something running. Again, head over to the GeoBase Reference Documentation. There's a tutorial that will be useful:
Alchemy Data Import Tool | Alchemy Tutorials | Importing Custom Data and Using it in GeoBase
'Chameleon' is the name that GeoBase uses for the map styles. There's a section in the documentation that should contain what you need. I think you'll probably be looking to use a brush object to color the ZIP code polygon, and a label object to name the ZIP code. Check out the Chameleon Workbench Tool, it makes creating and testing map styles really easy.
Let me know how you get on Rus, and do let me know if you run into any trouble or confusion.
Thanks for all the info. This is for a region maintenance screen of our app. We're about to start another agile sprint so we'll see if this is a priority or not. (Microsoft MapPoint is currently used, arg.)