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

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

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

Seva Lev's Problem Page  
   A collection of research problems.
   http://math2.haifa.ac.il/~seva/problems.html

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

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/

Open Problems  
   Some questions compiled by Jon Perry.
   http://www.users.globalnet.co.uk/~perry/maths/openproblems/openproblems.htm

Unsolved Problems and Conjectures  
   Regarding equal sums of like powers, compiled by Chen Shuwen.
   http://euler.free.fr/eslp/unsolve.htm