A few months ago I tried Tiny Tower and deleted it pretty quick. Didn't seem too interesting to me at the time. After hearing @Tungsten recommend, I installed it again.

Above I stitched together screen-shots of my Tower. I like that you can rename businesses whatever you want. The movie and video game store is named "Cheerful Ghost" and I named the cake store "The Cake is a Lie." I like that simple customization to your Tower. As you can see, I haven't quite come to name the new businesses at the top yet.

I generally never allow my apps to notify me when they have new business, but for this app I let it notify me for a few days with updates so I could build my tower at a regular pace.

Not playing it quite as heavy as I was but I still keep the Tower businesses stocked and move people up and down the floors. One interesting feature is the Bitbook where you can see what your residents are doing. Fun to see what they are posting, often times its not game related but interesting.