A highly useful component for all sorts of projects is the Microchip brand PIC (programmable integrated circuit). The chips contain a microcontroller, some RAM, and some storage space (quantities and speeds depend on the particular model). Basically - one chip can act as a tiny stand-alone computer with inputs and outputs for controlling other circuits. Most are programmable in-circuit allowing for updates to the code that is run. To program one, you will need to build or buy some sort of PIC programmer (specifics again vary by model of chip to be programmed). You will also need some software for compiling code (unless you want to write assembly - your choice!) and sending it to the PIC. Microchip itself provides a free integrated devolpment kit (IDE) called MPLAB that works very well.
If you are having troubles coming up with uses for this highly versatile devices, there are many ideas and projects out there. Good luck!