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I would think that Wiktionary (the dictionary from the folks that originally built Wikipedia) would fit the bill nicely.
API documentation for Wiktionary: http://en.wiktionary.org/w/api.php
Most API providers require registration to prevent denial of service attacks and other abuses. That being said, I did run across one that is available without registration:
Aonaware - This Web Service allows you to access dictionary definitions from the dict.org service.