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Open Problems in Dynamical Systems
http://www.math.sunysb.edu/dynamics/open.html
A collection of papers outlining unsolved problems maintained at Stony Brook.
Open Problems in Dynamical Systems and Ergodic The
http://www.math.iupui.edu/~mmisiure/open/
Originally from the Katsiveli 2000 Open Problems Session, now maintained by Sergiy Kolyada. PDF/PS.
The Furstenburg Conjecture and Rigidity
http://aimath.org/WWN/furstenburg/
If two commuting endomorphisms of a torus are incommensurable (no power of one is a power of the other), then their joint action should be rigid. Some of the conjectures and open problems compiled by the AIM.