Programs like iZotope RX (izotope.com; $349) “fingerprint” noise so you can subtract it from the audio file. But sometimes the noise is too interesting to throw away.
One of my favorite ways to get fresh sounds is to use controls backwards. For example, instead of throwing away the ums I cut from interviews, I transform this “garbage” audio into vocal grooves (see “Sound Design Workshop: Um's the Word” in the February 2008 issue, available at emusician.com). Similarly, most noise-reduction software has a button that lets you hear what the program is about to remove. The idea is to ensure that you aren't deleting too much of the signal along with the noise. But often this rumble and hiss has a cool, otherworldly character, particularly if you do cut into the signal a bit. I've used the extracted noise for ambiences and even applied rhythmic gating to create percussion parts that seem to speak.
If your noise-reduction program can preview the noise but not export it, try capturing the output with a stream ripper (see the November 2008 “Option-Click”) or a virtual audio cable such as Cycling '74 Soundflower (soundflower.com; free).