I found a couple of ways to do this with web based APIs. I think the US Postal Service would be the most accurate, since Zip codes are their thing, but Ziptastic looks much easier.
Using the US Postal Service HTTP/XML API
According to this page on the US Postal Service website which documents their XML based web API, specifically Section 4.0 (page 22) of this PDF document, they have a URL where you can send an XML request containing a 5 digit Zip Code and they will respond with an XML document containing the corresponding City and State.
According to their documentation, here's what you would send:
http://SERVERNAME/ShippingAPITest.dll?API=CityStateLookup&XML=<CityStateLookupRequest%20USERID="xxxxxxx"><ZipCode ID= "0"><Zip5>90210</Zip5></ZipCode></CityStateLookupRequest>
And here's what you would receive back:
<?xml version="1.0"?>
<CityStateLookupResponse>
<ZipCode ID="0">
<Zip5>90210</Zip5>
<City>BEVERLY HILLS</City>
<State>CA</State>
</ZipCode>
</CityStateLookupResponse>
USPS does require that you register with them before you can use the API, but, as far as I could tell, there is no charge for access. By the way, their API has some other features: you can do Address Standardization and Zip Code Lookup, as well as the whole suite of tracking, shipping, labels, etc.
Using the Ziptastic HTTP/JSON API
This is a pretty new service, but according to their documentation, it looks like all you need to do is send a GET request to http://ziptasticapi.com, like so:
GET http://ziptasticapi.com/48867
And they will return a JSON object along the lines of:
{"country": "US", "state": "MI", "city": "OWOSSO"}
Indeed, it works. You can test this from a command line by doing something like:
curl http://ziptasticapi.com/48867
