Is p-bromophenol more acidic than p-chlorophenol?
Disclaimer: This is not necessarily the "correct" answer as many factors play roles and it would be difficult to describe the observation so simply.

I'm not sure I can provide an easily "correct" answer, but I can try to explain some of the many factors that influence the acidity. 

Most notably, the factors we should consider are inductive effects and delocalization of charge.

The inductive effects, based on electronegativity, would dismiss the experimental observation, so I'll look at delocalization of charge.

The delocalization of charge, which introduces a negative charge by the halogen is greatest by F>Cl>Br>I. This would reduce acidity, as a more negative benzene ring would not desire to gain another negative charge. Thus, this is one factor that supports the experimental observation.

Thus, we may be able to explain the observation, if only partially, by the delocalization of charge.

I adapted the answer to a similar question on http://www.quora.com/Organic-Chemistry/Which-is-more-acidic-ortho-fluorophenol-ortho-chlorophenol-ortho-bromophenol-or-ortho-iodophenol-Why . I would have preferred more sources but I could not find a very good source.