Among the many choices one might get from an Internet search, I suggest Unsolved Problems in Geometry by Hallard Croft, Kenneth Falconer, and Richard Guy (Springer-Verlag, 1991). It may include references to non-Euclidean geometries.
As an aside, I would like to see a geometric proof that the configuration of Pappus is implied by that of Desargues for finite geometric spaces.
Gerhard "Ask Me About System Design" Paseman, 2011.01.30
