Does bit commitment yield oblivious transfer in the information-theoretic security model? Suppose you have two arbitrarily powerful participants who don't trust each other. They have access to bit commitment (e.g., sealed envelopes containing data that one player can hand to the other but that can't be opened until the first player gives the second a key). Can you use this to build an oblivious transfer protocol. Is this true even if the players agree to open all the envelopes at the end to detect cheating (e.g., after the poker hand is played, everybody agrees to reveal their cards)? 

I assume that you can't get oblivious transfer out of bit commitment, because oblivious transfer is cryptographically universal, and I can't find any references that say bit commitment is, but is there a proof somewhere that you can't do it?

Finally, has anybody looked at the problem if the players are quantum?
No, commitment has strictly lower complexity than OT. I think an easy way to see this is the approach taken in Complexity of Multiparty Computation Problems: The Case of 2-Party Symmetric Secure Function Evaluation by Maji, Prabhakaran, Rosulek in TCC 2009 (disclaimer: self promotion!). In that paper we have a result characterizing what you can do given access to ideal commitment in the UC model with statistical security.

Suppose there were a statistically secure protocol (against malicious adversaries) $\pi$ for OT using access to ideal black-box bit commitment. Then $\pi$ must be secure against honest-but-curious adversaries as well (not as trivial as it probably sounds, but not very difficult to show either). But you could compose $\pi$ with the trivial honest-but-curious protocol for commitment, and have an honest-but-curious OT protocol that is statistically secure with no setups. But this is known to be impossible.

Another way to see it is through Impagliazzo-Rudich. If you have computationally unbounded parties and a random oracle, you can do commitment (since all you need are one-way functions) but you cannot do things like key agreement, and thus not OT.