The following Kickstarter-funded projects all involve an adaptation of the popular and cheap Raspberry Pi, which just might inspire you to think of your own new application.
Dexter Industries BrickPi
Raspberry Pi and robotics are no strangers to each other, and Dexter Industries has managed to incorporate the board into a unique and modular LEGO-based robot. The company's add-on board connects to the Pi, provides ports for four LEGO Mindstorm NXT motors, five analog and/or digital sensors, and provides power (through a 9V power adapter) to both the Pi as well as the BrickPi, eliminating the need for a constant connection tethering the robot to a wall.
The Raspberry Pi acts as the robot's brain and can be programmed by the user in Python, Scratch, and C code (available on GitHub). The Pi and BrickPi are housed inside of an enclosure that allows the connection of LEGO Technic bricks, providing for a wide range of possible robot designs from grasping arms and ball canons to rovers and tanks.
With all projects, there are drawbacks. For the BrickPi, it's a controlling issue. Unfortunately, there has yet to be an app that allows users to control their creations directly without the need for programming. Dexter Industries controls its through direct input using a terminal application, but then again, aren't robots supposed to be autonomous? The BrickPi kit is available for pre-order on the company's website for $65, which nets you the board plus the case. Other components are priced separately.