Ayask, basically just take any basic sensor you can think of and try to find something to do with it.
Like the POT example Torben gave, you could attach a POT to MANY things and cause a circuit to activate when it reached a certain spot. You could attach it to a door to determine how far open or closed it was. You could remove the stops on the pot so that it worked for continous rotation and use it on a wheel to determine it's rotation. You can use a CDS cell or photo diode to measure light and turn a device on or off with it, night lights are a very common first project. Perhaps mix the two together and you could have an alarm sound if the lights were off and a door opened as a sort of simple alarm circuit.
You could use a microphone fed into an opamp intergrator and have it turn something on when the volume is over a certain level for a length of time.
These are just a few simple examples. Another way of thinking about it is to not think of what you can do with the circuit, but think of a problem that you think needs a sollution and see if you can come up with something that would use your electronics parts as a solution. That's how invention works. Inventors don't sit and stare at a pile of parts and think 'what can I make with this' they always start with a problem they think needs to be fixed and then find out what combination of parts and methods could be used to solve the problem.