Is there any free dictionary API that doesn't require API keys, and allows you to choose between multiple source and destination languages (as many as possible, at least English, German, Spanish, French...)?
You can try http://glosbe.com/a-api , it's big -- almost all languages covered. It allows you to access data in JSON/JSONP/XML. There is some limit set for users without key, but you can overcome it by using JSONP on your client side.