You have to work to the strengths of the lens and away from its weaknesses. The main weaknesses of the 18-55 are softness when wide open at either end of the range, lack of "reach" (which is immediately why a lot of newbs want to dump it and move on), and the smallish max. aperture. So, you don't want to try and use it for handheld lowlight shots without a flash (preferably off-camera flash), for thin DoF images (except possibly at macro distances), or for subjects you wish you were closer to.
However. If you stop the lens down one or two stops from wide open (e.g., f/8 @55mm), you can get some amazing things. If you add a flash or a tripod you can do low light shots that will be crisp and clean if you have good technique. It's a very good landscape lens. It's so small, light, and cheap that it's a great travel lens--and the focal length range is exactly suited to those stand-in-front-of-something-famous-I-was-there vacation shots most folks buy a camera for. It goes all the way out to 18mm. Use it at the wide end, stop it down, put it on a tripod, find some foreground interest, or shoot in a small space, and surprisingly good things can happen.
Post-processing and f/8 are the great equalizers among glass. Yes, you can find more expensive lenses that will do a much better job @18mm at f/3.5. But at f/8--it's gonna be a lot harder to tell the expensive glass from the budget glass. And no lens is going to limit you from doing HDR, noise-reduction, sharpening, or saturation boosting in post. Think of subjects you can shoot with the lens at 18mm and f/8, and you'll get closer to seeing what the kit lens can do.
One thing to try is googling up images taken with the kit lens, such as dpreview's "Kit Lens Losers" or the Flickr 18-55 kit lens group's pool. What may quickly become evident is that it's the skill of the photographer, not so much the lens that's making the image.