[silentrob]

I think you are describing TREC[1]. Over on the chatbot arena, there is The Loebner Prize[2], also interesting, but in general the systems are over learned.

[1] http://trec.nist.gov/ [2] www.loebner.net/Prizef/loebner-prize.html

[gojomo]

TREC, as far as I know, doesn't have a competitive question-answering format, with definitive right or wrong answers.

Jeopardy is a widely-understood game format; a competition-via-API would be understandable to a wide variety of competitors, from leading researchers to precocious cranks.

[nl]

There's TREC QA, which finished in 2007[1]. This year they are doing TREC Live QA[2] (which looks pretty challenging!)

Outside TREC, there is the CLEF QA track[3]

[1] http://trec.nist.gov/data/qamain.html

[2] https://sites.google.com/site/trecliveqa2015/

[3] http://nlp.uned.es/clef-qa/