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http://www.csse.uwa.edu.au/~gordon/remote/questions.html

Colouring, algebraic graph theory, geometries.

http://www.imada.sdu.dk/Research/Graphcol/

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.

Graph Theory Open Problems

http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html

Six problems suitable for undergraduate research projects.

Open Problems in Graph Algorithms

http://www.vuse.vanderbilt.edu/~spin/open.html

Compiled by Jerry Spinrad.

Past Open Problems Columns

http://www.math.uiuc.edu/~west/pcol/pcolink.html

By Douglas B. West, from the SIAM Activity Group Newsletter in Discrete Mathematics.

Perfect Graphs

http://www.aimath.org/WWN/perfectgraph/

Conjectures and open problems, maintained at the AIM.

Perfect Problems

http://www.cs.concordia.ca/~chvatal/perfect/problems.html

Unsolved problems on perfect graphs.

Problem of the Month

http://vega.fmf.uni-lj.si/~mohar/Problems.html

Research problems collected by Bojan Mohar.

Problems in Graph Theory

http://www.maths.qmw.ac.uk/~pjc/oldprob.html

Maintained by Peter Cameron.

Problems in Signed, Gain, and Biased Graphs

http://www.math.binghamton.edu/zaslav/Bsg/sgbgprobs.html

Compiled by Thomas Zaslavsky.

Problems in Topological Graph Theory

http://www.emba.uvm.edu/~archdeac/newlist/problems.html

Web text by Dan Archdeacon with a list of open questions in topological graph theory.

Some Open Problems

http://www.eecs.umich.edu/~qstout/constantques.html

Open problems and conjectures concerning the determination of properties of families of graphs.

Some Open Problems

http://www.louisville.edu/~aekezd01/open/open.html

Kézdy's open problems.

Some Open Problems in Graph Theory

http://io.uwinnipeg.ca/~ooellerm/open_problems/index.html

Open Problems involving Steiner distance.

Three for the Money: The Degree/Diameter Problem

http://www.c3.lanl.gov/mega-math/workbk/graph/grthree.html

Students can understand and work on an unsolved problem in mathematics.

Unsolved Problems

http://www.math.fau.edu/locke/unsolved.htm

Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke.