Ticket to Ride New York. 5 minutes to explain. 20 minutes to play, 5 each setup/takedown. Simple in the mechanics. The strategies, however, are as in depth as the 1-2 hours of the larger TTR games.
Carcassonne - most can be played (using only the basic set) in 30-40 minutes, and the rules can be explained in 5 min.
Great Khan Game: plenty of depth - 7-10 min explanation, 20-60 min play time.
8 Minute Empires. 5-10 min explain time, 20-40 min playtime. (the name is hyperbole...)
Photosafari - 5 min explain, 15 min play time. much replay value.
Odin's Ravens: 3 min explain. 15 to 30 min play time. "It's candyland for adults"
Elkfest: 3 min to explain, 5 to 60 min, depending upon relative skills. (Dexterity game)
Any of a dozen whist variants. 5-7 min to explain.
plenty of short, non-shallow, simple to teach games available.
Monopoly: 5 min to setup. 2 min to explain. 1 min to throw that game on the floor because it's awful.