I'm not the creative type, so to me a flash gun is really just a tool to meet a need. If the need is not there I do not use it. I don't go out of my way to invent reasons to use my flash guns, other than to experiment with technique and see what it can do. There are some examples of my experiments here. See posts 14-15...
http://photography-on-the.net/forum/showthread.php?t=499526
The benefit of the external flash is not so much in just having a more powerful flash still stuck to your camera. The power of the flash really comes into its own when you can move it off camera and make the light come from the direction you want and not simply where the camera is. A flash with a tilt/swivel head will allow you to bounce light off ceilings and walls, to create a soft light, with no harsh shadows, when shooting people and things indoors. If your flash does not have a tilt/swivel head then a simple off-camera flash cord will allow you to hold the flash in your left hand and the camera in your right. You can aim the flash wherever you like and adjust the point of origin (a bit).
Check out this guy's technique -
http://www.youtube.com/watch?v=tQKqj4W0QWI
With a more powerful unit, that can be run off-camera, you have the opportunity to change the light with diffusers and reflectors. You can get a nice portrait setup with one flash and diffuser on one side of your subject and a reflector on the other side. The flash does need to go off-camera to do this kind of thing.
You can use the flash to freeze subject motion, even when the ambient light is low. If you shoot the first dance at a wedding, for example, set a slightly long eposure - maybe 1/20 or 1/10 second to capture the ambience of the background - people will be dimly burred - but use flash on your subjects to pick them out and freeze their motion in the frame.
If you have 2nd shutter sync available you can create motion effects, say of a car moving forward, where a faint streak is captured as the car moves forward and then your flash fires as the second shutter closes and you freeze and fully illuminate the car at the front of its streak.
For more inspiration, try these sites....
http://www.dg28.com/technique/index.htm
http://planetneil.com/tangents/flash-photography-techniques/
http://www.strobist.blogspot.com/
There is a massive small lighting (flash) forum over on POTN. It is Canon based but there is loads of good stuff about general technique as well. Sample post here....
http://photography-on-the.net/forum/showthread.php?t=426102