This must be a common problem because I see it in many published papers but it seems to be quite tricky to google for. You can insert a bibliography like so
\bibliographystyle{plain}
\bibliography{foo}
and everything works as expected except there is sometimes (I have no idea what circumstances cause this -- it seems random to me) no space between the section heading (e.g., "7. References") and the start of the actual references. The section heading and first citation appear all squished together. It's not utterly egregious but seems to me to be unambiguously a flaw in the typesetting.
I've been putting up with it for years but someone somewhere must have noticed this and been obsessive-compulsive enough to track it down and figure out what causes it and how to correct it.
I thought this would be a good place to record the solution. Let me know if you can think of ways to make this more googlable.
ADDED: Here is an example document exhibiting the problem: http://yootles.com/outbox/squish/. (See also my workaround below.)