Tiny Tower is a game that had me glued to it for a good two battery drains over Thanksgiving, which is to say about 20 hours of post-carb gaming insanity.
In it, you play the role of building manager, elevator attendant, shipping and stocking coordinator, rental agent, and therapist to the stores and residents of a tower you continually guide and grow. You start off in the tutorial with a small amount of cash and build an apartment and a store and get a couple of people into the former and make them work at the latter.
From there on out your objective is to make cash, expand the building, and make everyone happy. You earn money by collecting rent from your tenants and as a portion of every sale the businesses in your building make. Each business can employ up to three people, and each person is capable of stocking one additional item. Items take various times to stock; the longer it takes an item to stock the more it usually goes for in the end, but you can only stock one item at a time.
You can cut stocking and building times by spending something called Tower Bucks, which you get for completing various tasks such as finding a tenant to deliver a box of puppies to, getting someone to the right floor, or building another level on the tower.
Along the way, various VIPs will show up. I've found four different types of them so far: he stocking VIP who drops restocking times by three hours, the big spender who buys out all of one product on a floor you deliver him to, the construction worker who knocks hours off of floor construction, and the celebrity who causes drones of people to flock to wherever you deliver him.
The game is free, although you can purchase Tower Bucks if you don't want to work to get them, which involves purchasing Mobage Coins from their market for cash, then transferring them into Tower Bucks. I have not found thus far, at 15 stories of my building, that I needed to do much more than play a little longer to get what I needed, but your mileage may vary.
Tiny Tower claims to be the #1 iPhone game, and although I can't find anything that backs up this claim, I would not doubt that at all. As with many other popular iPhone games, a company called Mobage is handling the port from iOS to Android.
I have some issues with Mobage stemming from their port of Zombie Farm (along with a few other apps in the Market), which suddenly started asking for superuser permissions. After 11 days and 3 elevations, their support team has been unable to tell me why their app is calling a third-party program. In short, this is not a company I would personally trust with a credit card or on any rooted phone that has Superuser set to auto-allow, as they don't seem to have a good grasp of what they're doing just quite yet. Mobage's Superuser issue did not make it to Tiny Tower, and I don't think it's malicious (probably just a library they included), but it's just something to keep in mind if you're rooted.
In short, Tiny Tower is wickedly fun, brilliant little game. It takes a lot to get more than an hour or two out of me (I'm looking at you, Fieldrunners.)