The book Research problems in discrete geometry by Peter Brass, W. O. J. Moser, János Pach, is a very large collection which describes what is known about each problem with a large reference list of papers for each problem.
Also Google Books search: "open problems in" OR "unsolved problems in" OR "research problems in" mathematics
and Google Scholar search: "open problems in" OR "unsolved problems in" OR "research problems in" mathematics