I actually played Tiny Tower for the first time back at GDC this year -- the guys at NimbleBit kindly showed me an early version of it while they were in the middle of designing the game. The title itself is now out and finished on the App Store, and after having played it for about a week already (thanks to a press preview), I can say it's an amazing title that's made even better by the fact that it's completely free to install and play.
It's very much like the old SimTower game in that you create and run a tower filled with little characters called Bitizens. You can build residential floors to move Bitizens into, and then you can put them to work on other floors that fill out certain categories, like retail floors and services and recreation areas. You can assign three Bitizens to work on a certain floor, and then you pay money to stock goods in those stores and sell them to various visitors.
In addition to the time-based management side of the game, there are a few games to play, like getting Bitizens to the right floor in a working elevator or playing find-the-Bitizen. These games are more integrated into the overall game than, say, the pond was in NimbleBit's Pocket Frogs, but I'm still a little disappointed that they don't have too much of an effect. You can make a few bucks at a time, and there are VIPs that show up every once in a while, but the floors you deliver people to don't seem to really have a direct effect.
Nevertheless, it's fun building up your tower, and while the push notifications (if you keep them on) threaten to get annoying after a while, the amount of detail and care put into the art and strategy is excellent. There are even little extras, like a "BitBook" social network page and a fun screen to compare your friends' towers via Game Center. Tiny Tower is yet another great title from NimbleBit. It's a freemium download (and like Pocket Frogs, you can buy "convenience currency" with an in-app purchase, but I haven't needed it yet) that's available right now.