CARROT (US$0.99) is essentially a game with delusions of productivity. In fact, it was initially pitched to me as a utility app with "personality."
That's problematic because it's not really all that useful. What it is, though, is silly fun with occasional side benefits of getting things done.
I hand-picked the screen shot that goes with this post to reflect my "aha" moment. It's when I finally realized there was no way this app was actually interested in helping me organize my life and work.
Once I relaxed and let go, CARROT was able to win me over with its charm and superb design. Your tolerance for Kawaii (かわいい, namely, that which is "lovable," "cute" or "adorable," according to Wikipedia) will influence how much you love or hate this app.
CARROT is, frankly, twisted. It's basically GLaDOS as digital personal assistant. Your job is to keep it pleased, by finishing assigned tasks and keeping your work in order.
I made sure to add "Buy cake and hire grief counselors" to my CARROT to-do list.
The following video demonstrates the app in action.