Ever wondered how they get shadow-free product photos? Some of the best I've seen are those over at Sparkfun. Well, normally, photos like those are taken inside a light tent with illumination from all sides, including underneath. This eliminates shadows, and the white background of the tent makes it easy to clip the item out of the background.
Lacking a light tent, here's a trick which results in a pretty decent photo. Suspend whatever it is you're photographing with some strands of clear nylon fishing line (easy to Photoshop out afterwards). Set up the camera so it's focused on the item in question, and then place a piece of white cloth material behind the item, but far enough away that the white cloth is out of focus (so it appears as a reasonably smooth white background). Obviously, if there is a direct shadow cast by the hanging item, make sure that it isn't in the field of view of the camera. An alternative to fishing line might be to place it on a piece of glass, but you might get relflections from the glass.
Use whatever illumination you feel happiest with - incandescent, fluorescent, or natural daylight. Try and avoid bright sunlight, because it seems to give a lot of glare. The best I've found is a bright but cloudy day. Plenty of light, but mostly diffuse.
Here's an example of what can be done. The fishing line, background, and any blemishes have been removed with Photoshop's touchup tools. The background has been erased to transparent, so the photo can be placed on any background and still look reasonable. When rubbing out the background, use the eraser tool with a feather edge - this ensures that the final image also has a feathered edge so it blends better into the background.