Hilbert's address was more than a collection of problems. It outlined his philosophy of mathematics and proposed problems important to his philosophy.
Although almost a century old, Hilbert's address is still important and should be read (at least in part) by anyone interested in pursuing research in mathematics.
In 1974 a symposium was held at Northern Illinois University on the Mathematical developments arising from Hilbert problems. A major mathematician discussed progress on each problem and how work on the problem has influenced mathematics. Also, 23 new problems of importance were described. The two-volume proceedings of the symposium was edited by Felix Browder and published by the American mathematical Society in 1976. See also Irving Kaplansky's Hilbert's problems, University of Chicago, Chicago, 1977.
There is also a collection on Hilbert's Problems, edited by P. S. Alexandrov, Nauka, Moscow, 1969, in Russion, which has been translated into German.
David E. Joyce
Department of Mathematics and Computer Science
Worcester, MA 01610
These files are located at http://aleph0.clarku.edu/~djoyce/hilbert/