Graph Theory Open Problems  
   Six problems suitable for undergraduate research projects.
   http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html

Unsolved Problems  
   Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke.
   http://www.math.fau.edu/locke/unsolved.htm

Open Problems in Graph Algorithms  
   Compiled by Jerry Spinrad.
   http://www.vuse.vanderbilt.edu/~spin/open.html

Three for the Money: The Degree/Diameter Problem  
   Students can understand and work on an unsolved problem in mathematics.
   http://www.c3.lanl.gov/mega-math/workbk/graph/grthree.html

Problems in Signed, Gain, and Biased Graphs  
   Compiled by Thomas Zaslavsky.
   http://www.math.binghamton.edu/zaslav/Bsg/sgbgprobs.html

Problems in Graph Theory  
   Maintained by Peter Cameron.
   http://www.maths.qmw.ac.uk/~pjc/oldprob.html

Problems in Topological Graph Theory  
   Web text by Dan Archdeacon with a list of open questions in topological graph theory.
   http://www.emba.uvm.edu/~archdeac/newlist/problems.html

Graph Coloring Problems  
   Archive for the book "Graph Coloring Problems" by Tommy R. Jensen and Bjarne Toft (Wiley Interscience 1995), dedicated to Paul Erdös. Gives progress and new problems.
   http://www.imada.sdu.dk/Research/Graphcol/

Past Open Problems Columns  
   By Douglas B. West, from the SIAM Activity Group Newsletter in Discrete Mathematics.
   http://www.math.uiuc.edu/~west/pcol/pcolink.html

Perfect Graphs  
   Conjectures and open problems, maintained at the AIM.
   http://www.aimath.org/WWN/perfectgraph/

Problem of the Month  
   Research problems collected by Bojan Mohar.
   http://vega.fmf.uni-lj.si/~mohar/Problems.html

Perfect Problems  
   Unsolved problems on perfect graphs.
   http://www.cs.concordia.ca/~chvatal/perfect/problems.html

Gordon Royle's Open Questions  
   Colouring, algebraic graph theory, geometries.
   http://www.csse.uwa.edu.au/~gordon/remote/questions.html

Some Open Problems  
   Kézdy's open problems.
   http://www.louisville.edu/~aekezd01/open/open.html

Some Open Problems in Graph Theory  
   Open Problems involving Steiner distance.
   http://io.uwinnipeg.ca/~ooellerm/open_problems/index.html