About a year or so ago, my brother introduced me to the strategy game Ticket to Ride. It is a ton of fun to play. It has elements of what make games like Risk or Settlers of Catan fun (strategy, planning, sabotaging competitors) but is a shorter game, less involved, so it's easier to play and the games go by more quickly. My older daughter can follow the game play and even do ok without help (never winning, but not always losing), but it's challenging enough for the adults in my family to enjoy.
I recently had a chance to try out Ticket to Ride, an app available for Apple and Android. It is just as much fun as the board game, plus it's much easier to take along! The computer opponents are competitive but not overly challenging (I win about half the games I play). The gameplay is quicker than with a board game, since pieces don't actually have to be moved. There are online and "pass and play" options (which I've used while waiting in line) and there are also options to upgrade to different maps and other features.
For those who play the board game, it's a fun way to bring the strategy in a very portable way. For those who don't, it's a great way to get introduced to a fun board game!