Note that clipping paths give you a sharp edge, so your feathering will be lost. To keep the feathering, it depends on what application you're bringing it into:
Photoshop - Make sure it's on a transparent background, and save it in a format that supports transparency (such as PSD).
InDesign / Illustrator - You should be able to import PSD files into these apps and retain the transparency information.
QuarkXPress - I haven't tried Quark 6.5 yet, but previous versions had to real variable transparency features. In this case, as Eggles said, you must either use a clipping path, or add the background to the Photoshop file before importing.
The Web - Only two common formats support transparency: GIF (poor quality, widely supported) or PNG (great quality, not as widely supported). Use the Save For Web function to try out what's best for you.