Google Search by Image API?

You can easily search by an existing image by inserting this into your address bar:

https://www.google.com/searchbyimage?site=search&sa=X&image_url=YOUR_IMAGE_URL

Example:

https://www.google.com/searchbyimage?site=search&sa=X&image_url=http://cdn.sstatic.net/Sites/stackoverflow/company/img/logos/so/so-icon.png

Sorry to say, but the Google image API is deprecated:

Important: The Google Image Search API has been officially deprecated as of May 26, 2011. It will continue to work as per our deprecation policy, but the number of requests you may make per day may be limited.

Quite sure there are some alternatives (http://www.tineye.com/ and http://mrisa.mage.me.uk)

Update (2013): There is now Google Custom Search which allows image searches.