Is there an evolutionary advantage to crying when sad?
First, here is a link to an article that discussion the answer to your question:
Why Cry? Evolutionary Biologists Show Crying Can Strengthen Relationships

The original article to which it refers can be found here:
Emotional Tears as Biological Signals

To speculate a bit on Jez's question, crying in adults could be a result of our possible Neoteny. Crying in infant animals is extremely common as a way to elicit attention and sympathy from the mother. If we are neotenous apes, crying could be a left-over behavior that was seized by evolution, instead of being discarded.