For starters, you've got the classic role-playing game mechanics - kill zombies, get experience points, level up, improve skills, and upgrade weapons. Since the app is location aware, you're fighting zombies at real-world locales pulled from Foursquare, and some spots have better loot to scavenge than others. You can build up strongholds to travel between, and upgrade them with added defenses. Even if you don't get out much, you can designate your home or work as a safe house, and invite your friends to slay along with you. There's a chat system in place too, so you can keep tabs on what's going on. If you're just playing on your own, there's an ongoing story to follow, complete with graphic novel cinematics, and it'll be updated regularly with episodic content. If you're the competitive type, you can duel other survivors, and soon, they'll have safehouse versus safehouse combat. Eventually, they'll have a crafting system and vehicles in place too. Please Stay Calm also comes complete with OpenFeint and Game Center support if you want to keep in touch with your buddies.
In a lot of ways, Please Stay Calm looks like my ideal smartphone game; it's multiplayer, it's location-aware, it's got persistent rewards, it's free, and it's got beating the snot out of damn, dirty zombies. What's not to like? Well, it's not on Android or BlackBerry. That's a bit of a downer.