Currently (March 2016) the only freely available translation API is Bing Translator. It is free for a bit over 1000 pages (2 million characters) per month. Bing's quality is good, even better than Google's in the languages that we have researched (Machine Translation Quality Statistics).

For European public service organizations the EU's machine translation is available, currently for free (Machine translation for public administrations - MT@EC). This is likely to remain free for its users although this hasn't been decided officially yet.

Of course, access to Moses machine translation technology (Moses - Main/HomePage) is free but that requires you training your own machine translation engine (i.e. requires much bilingual data and some skills).

Google Translate is no longer free. As far as I know, all other MT APIs are also paid services.