Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single volume, complete with bounties where applicable. Of course Erdos posed many other open problems in combinatorics and number theory that do not appear in this book. I once heard a rumor that some people were working on a project to publish a similar but more comprehensive book or series of books, covering all of Erdos's open problems, but I don't know if the rumor is true. Does such a compilation exist? If not, is there anything else like this besides Chung and Graham's book?
I would be most impressed if there existed such a list! The closest thing I've found is this long list of references to papers Erdős published containing problems. I don't know if it is comprehensive, and it has some overlap with the content of Chung and Graham's book, but it at least contains the names of the Erdős papers cited in Guy's Unsolved Problems in Number Theory.
Although not an answer to the original question, but let me mention that Erdos' papers up to 1989 are available here.
This is not a direct answer to your (good!) question, but Research Problems in Discrete Geometry by Brass, Moser, and Pach (Springer 2005) cites Erdős more than 100 times.
For graph theory problems, I find this the most comprehensive resource: http://www.math.ucsd.edu/~erdosproblems/