Seva Lev's Problem Page
A collection of research problems. http://math2.haifa.ac.il/~seva/problems.html
Unsolved Problems and Conjectures
Regarding equal sums of like powers, compiled by Chen Shuwen. http://euler.free.fr/eslp/unsolve.htm
Unsolved Problems and Rewards
By Clark Kimberling. Offers prizes for solutions of some problems in number theory. http://faculty.evansville.edu/ck6/integer/unsolved.html
Open Problems
Some questions compiled by Jon Perry. http://www.users.globalnet.co.uk/~perry/maths/openproblems/openproblems.htm
Number Theory Conjectures
A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references. http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html
L-functions and Random Matrix Theory
Conjectures and open problems concerning L-functions, focussing on the areas in which there has been recent progress using results from Random Matrix Theory. Maintained at AIM. http://www.aimath.org/WWN/lrmt/
Mathematician's Secret Room
Unsolved problems in Number Theory. English and Japanese text by Hisanori Mishima. http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm
Advice to Research Students
Some tips for solving problems in number theory, collected by the Cardiff University group. http://www.cf.ac.uk/maths/numbertheory/problems.html
The Computer Science Directory currently has categories, which include links along with indexed pages.