Today's pickup game just barely qualifies, as games can take more than a few minutes, but I included it because it's turn-based and easy to get back into in case you do have to stop mid-game. It's Reiner Knizia's Samurai, a computerized version of the popular board game, and it even has an OS X version.
Samurai is a game for 1-4 players that takes place on a hex-tiled board representing feudal Japan. The goal of the game is to unite Japan by garnering the most support from the three castes: monks, farmers, and nobles. The board is filled with villages and cities that are represented by the castes. Most villages are represented by one caste, but there are some that have two and the big city Edo has a representative for all three.
You gain the support of a village's caste by laying down influence tiles next to it. You have samurai, which act as influence to any of the three castes, as well as caste-specific influence tiles. There are also boats that can be placed near coastal villages for an extra one or two influence. Once a village's adjacent land tiles are all occupied, the caste in that village pledges support to the player who has the most influence.
There are some additional special tiles and a few extra rules, but the tutorial included with the game will explain them better than I can. It does a very good job of teaching the game's rules, showing the board as it explains what's happening.
Games of Samurai can be fairly short, and the AI provides a good challenge across three different difficulty levels. There are also internet and hotseat (taking turns at the keyboard) multiplayer options. The free trial version of the game gives you 10 plays of the game, and the full game is $19.95. Another polished presentation from a small company— give it a try.
Read [Samurai Info/Download Page]