Rich math tasks are open to encourage multiple methods, representations, and pathways.
Rich math tasks are inquiry based.
Rich math tasks allow students to experience the mathematics conceptually before procedures.
Rich math tasks have a visual component.
Rich math tasks are "low floor" and "high ceiling".
Rich math tasks require students to convince, reason, or justify.
Also see this spreadsheet that further breaks down some of Robert Kaplinsky's problems by standard.
(These are long tasks meant to assess student understanding and guide teaching mid-way through a unit.)
(These are not tasks, but could be used daily or weekly as short warm ups/exit tickets to encourage thinking & talking)