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Constructive Approximation Open Problems

http://www.cecm.sfu.ca/personal/pborwein/CA_MOSAIC/CA_problems.html

Research problems section of the journal, edited by Peter Borwein, Albert Cohen, Ingrid Daubechies and Vilmos Totik. Includes problem statement (PostScript) and discussion.

Favorite Unsolved Problems

http://www.math.purdue.edu/~eremenko/

Alexandre Eremenko (Purdue University). Mainly in analysis.

Open Problems in Linear Analysis and Probability

http://www.math.tamu.edu/research/workshops/linanalysis/problems.html

Problems taken from workshop lectures given at Texas A&M University.

Some Unsolved Problems

http://www.math.unibas.ch/~winkel/problem.html

Mainly in analysis. By Jörg Winkelmann.

Unsolved Problems in Function Theory

http://www.math.purdue.edu/~eremenko/uns.html

Notes by Alexandre Eremenko.