Posted this over on Flightinfo.com in a similar thread... don't know if it was you over there though, so I'll repost here...
~Josh
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A lot depends on how you handle the situation, exactly what you say, and what the reasoning was. However be advised that any time that you turn down/decline an interview, it means that most likely your resume will get "recycled" to the bottom of the stack at the very least.
If you are declining because of a conflict or other personal reason, then the best bet is to be as upfront about it as possible. (Say for example they call and want you there the next day and you can't make it, or have a family emergency, or other obligation- such as another interview). Odds are that if you are very forward and honest about the reason, it will be simple to reschedule. If you aren't willing to share that you have another interview, just simply state that you have another obligation that particular day and would appreciate greatly if you could reschedule.
If you're turning down an interview because of some other reason (say you've already accepted another position), the best thing to say is that you are unable to accept their invitation at this time, but you will notify them as soon as the situation changes and would appreciate it if they kept you on file. Odds are that they won't keep you in the "interview" pile, but it won't eliminate any future opportunities.
Whatever you do, DON'T BLOW THEM OFF and not show up for a scheduled interview. It's a surefire way to end up on a company's do not interview list.