Welcome to the forum.
Are we talking about a Teleconverter for an SLR camera with interchangeable lenses, or a teleconvertor that screws onto the front of a digi-cam lens?
Either way, image quality will be negatively affected. Almost anytime you add more glass for the light to pass through, you will be degrading the image quality...and yes, for top quality converters, the difference in quality is slight, and the average Joe may not notice.
Teleconverters for SLR cameras go behind the lens. A 2X teleconvertor will 'steal' about two stops of light....so it's best to use them with fast lenses (F2.8 or better). If you don't use fast lenses, the view finder will may be too dark to manual focus and that's important because there may not be enough light for the AF to work properly.
I have a 2X converter that I sometimes use on my 75-300 F4-5.6 lens...but AF usually doesn't work so I have to manually focus.
If we are talking about the front mounted adaptors for digi-cams...from what I hear, the quality isn't usually that great. You would be better off not using it and cropping an image instead. Of course, using a tripod will help to get sharper shots that are more suitable for cropping.