Eve API Proxy
I have created an API proxy service via Google's App Engine. You can access the proxy at http://eveapiproxy.appspot.com. The source code for what is running there is available via at http://code.google.com/p/eveapiproxy/ if you are interested.
If you don't know what this whole API thing is, you can understand how to use the proxy and read more here: http://myeve.eve-online.com/api/doc/. Basically, this proxy takes care of all the caching issues associated with API access. The proxy caches for you. Just use http://eveapiproxy.appspot.com in place of http://api.eve-online.com in your API calls. For example, the skill tree can be accessed via http://eveapiproxy.appspot.com/eve/SkillTree.xml.aspx. CCP's servers are hit only once for the data during CCP's suggested cache period.
You might be concerned about security. It is true that if I wanted to, I could browse through the data store and see the data you requested via the service. If you are concerned about this, don't use this service or any other API-related service. Alternatively, you could just copy the proxy code to your own Google App Engine account and run the proxy yourself. The code is open, and the tools/service is free.
My motivation here was primarily to try out Google's cloud computing offering. The price is right.
If you combine this service with the importXML(URL, XQuery) function available in Google Spreadsheets, you can create some pretty useful out-of-game utilities.
Finally, I am not a professional coder -- so feel free to throw me constructive criticism about the code at http://code.google.com/p/eveapiproxy/. I have also written a Java library for Eve applications, but that is for another post...
Eve Online Forum thread: 
Update: I fixed the POST vs. GET issue today with help from Dafire. The proxy should work with applications like EVEMon now. Aximag 00:08, 7 December 2009 (UTC)
Update: I incorporated zakuluka's patch to handle the Dominion APIs. Thanks zakuluka! Aximag 07:55, 16 January 2010 (UTC)
Update: Added support for research job API calls. Aximag 00:52, 25 January 2010 (UTC)