Android: Netrunner is a 2012 reboot of the classic collectible card game from the 90's, now redone as a "living card game" (meaning the base set is all you need to play, and expansion packs add to the fun in reliable ways rather than relying on the luck of buying a multitude of packs or, worse, going to ebay).
It's a two-player deck-builder set in a dystopian future of space elevators, genetic engineering and near-universal surveillance. One player is the Corporation, installing secret agendas in remote servers. The other is the Runner, a hacker bent on breaking in and stealing these agendas.
The box in the sidebar contains all you need to play with a friend. You can download the rules as a PDF. For the "show, don't tell" set, this video tutorial is great:
There's a great, free iOS app for tracking your Android: Netrunner play. It keeps track of clicks, credits, brain damage and more, allowing you to leave your chits at home and pack only your deck.
Ironically, there is no Android OS version as of this writing.
There's also a deck-building web app that makes it easy to try out combinations of different cards and share the results with your friends/enemies.
If you've tried out several factions and find yourself wanting more, there have been 6 expansion packs so far. Each one adds a new identity to one corporate and one runner faction, as well as a bunch of new card types that change gameplay in interesting ways.