Sites

Open Problems from the Geometry Junkyard (Popularity: )
http://www.ics.uci.edu/~eppstein/junkyard/open.html
Compiled by David Eppstein of the University of California at Irvine.

The Open Problems Project (Popularity: )
http://www.cs.smith.edu/~orourke/TOPP/
A project to record open problems of interest to researchers in computational geometry and related fields.

Open Problems (Popularity: )
http://compgeom.cs.uiuc.edu/~jeffe/open/
Collected by Jeff Erickson. Mainly in geometry.

Steiner Trees (Popularity: )
http://ganley.org/steiner/open.html
Open Problems with Steiner Trees, maintained by Joe Ganley.