Hero Academy is a game by Robot Entertainment. (They also made Orcs Must Die! and its sequel.) An asynchronous multiplayer game, which is to say that you take your turn, and then the game lets your opponent know that it's their turn. They take their turn when they have time, you take your turn when you have time, rinse & repeat until somebody wins.
It's a fairly simple strategy game - you have a grid-based map on which you and your opponent each have a number of crystals. By deploying offensive and defensive units on to the map, you try to destroy the crystals of your opponent by protecting your own. There are also items you can use to help your team, and spells, and units that have special abilities; a fair amount of variety and depth is contained within a simple formula.
For being varied and deep, though, Hero Academy plays fast. You always have a randomized "hand" of six units/items/spells to deploy, so you don't get overwhelmed by options, and matches don't take that many turns to play out (how long that'll take just depends on how quickly you and your opponent take your turns).
First launched on iPhone / iPad earlier this year, it started out as a fairly straightforward if quirky fantasy-themed affair. The developers have a sense of humor, though, and since the game's release they've added steampunk dwarves, brutish orcs, and - now that the game is on Steam - a team based around Team Fortress 2. Which doesn't make any sense, but it doesn't have to, because it's just a wacky good time and they aren't telling a story here. The result feels like a cartoony board game with tiny expansion packs, which I think is pretty great.
Take a couple minutes and check out the trailer.
If this looks like your thing, it's five measly dollars on Steam. Four dollars apiece if you buy two copies. And you can play against everybody who already owns the game on their iPhones / iPads. The purchase price gets you two of the teams - others are available for a few bucks more, but the game plays great just with the default set.
I've been playing Hero Academy for months on my iPhone, and it gets at least a little of my time almost every single day. Launching the game on Steam and allowing cross-platform play is a brilliant thing for Robot Entertainment to have done. I'm "Ravenlock" (on Steam and in this game). Buy it and play it with me. Thanks.