The idea here is to be able to use the arduino as an etch-a-sketch. Even if we cannot figure out how to output directly on an led beneath the touchscreen (that is, it would be used like a Wacom tablet instead of an actual touchscreen), we could create a program that allows the Arduino to communicate input to another program, such as Flash.
There are several options as to how to get a touchscreen. We could (as Le suggested) try to build one, or buy one online for under twenty dollars.
(Semi)Automated Plant Terrarium
I am really horrible at remembering to water and take care of my plants. So why not program the Arduino to do it for me? It might be able to measure sunlight levels and, hooked up to external solar lights, be able to adjust their levels as necessary. Or perhaps it can measure the dampness of the soil and send me an email when I need to water it.