For Australia, the Bureau of Statistics provides most of the information:
Country boundaries should be produced by merging all the state boundaries (below) into a single polygon feature.
State level boundaries are available.
County: The states can be geographically disaggregated in a number of ways - perhaps the most similar to county boundaries are Local Government Areas (LGAs).
City boundaries: To find the area of cities, the standard dataset to use is the urban centres and localities digital boundaries.
Zipcode boundaries: Zipcodes (or postcodes as they are known here) are more difficult to model. Because they are based on the rules by which Australia Post deliver the post, they are rather fuzzily defined. The free option approximates postcodes as the census collection district level, and is available for 2006 from the ABS.
Edit: the updated 2011 datasets and census results are available via the Data Packs section of the ABS site, which requires free registration.