I read somewhere once that there is a single word in some language,
possibly African, with a meaning similar to "a situation in which two
people, looking at each other, are each hoping that the other will
bring up some topic which both wish to discuss but are unwilling to
introduce." What is this word, what is the language, and where did you
find the information?

Hi alexiskai-ga,

The word that you're looking for is "mamihlapinatapei" from the Tierra
del Fuegan language (spoken in South America).  Numerous online
sources cite the Guinness Book of World Records as the "most succinct
word".

Sources:
They have a word for it: <http://www.worldwidewords.org/reviews/thawfi.htm>
Wikipedia: <http://en.wikipedia.org/wiki/Mamihlapinatapai>

I have heard of this word before, but don't remember what it was, so I
searched Wikipedia for "most untranslatable words", which eventually
led me to the entry for the word.

I hope this answers your question.  If you need clarification, please
request for it before rating this answer.

secret901-ga

Just what I was looking for.

Perhaps the saddest aspect of this is that there are now no native
Fuegans left - not even two to look into each other's eyes hoping to
bring up a topic neither wishes to initiate.