I don't mind some complexity, but I would like to learn the game well enough in 30-60 minutes. I have definitely lost patience with new board games where some friends and I spend our entire evening just learning to play rather than playing.
I think the ColdWar Commander / Blitzkrieg Commander games can be picked up in that time. Movement, command, and combat rules are quick and intuitive, and it generally lends itself to a "resolve-problem-by-common-sense" approach. It's great for casual gaming.
http://backtominnesota.com/Ancients%20Old/Old%20Ancients.htm
(Or my all-in-one file, here: http://suspended-chord.info/static/downloads/paperparachute-...)