A toothbrush timer for kids?
You can have a nice "animation-tooth-bot" with just a few servo's, an Arduino and a toy doll.
An alarm clock which wakes you 10 minutes earlier if your need to scratch ice from your cars window.
And is synchronized with your digital agenda so if you have a day off it does not ring at 06:00
A tool that switch off the lights when there is no movement for 5 minutes.
They all share the same pattern, do something meaningful after some amount of time, a certain trigger or both.