Is there a program that can edit sound on the fly?

For instance if I am recording video in a studio, can I have the mic running to a PC, then add effects or do noise reduction etc, and then have it go to the camera to be recorded?

Lots of them, but latency is an issue in most cases. CastBlaster, for instance, does this with minimal latency and access to a sound library. No Noise Reduction possibility, but it'll do it.
Sony Vegas also does this easily, but the problem there, is putting in your FX if you don't know where they'll be. I did see one guy using a second instance of Vegas open on the same computer with regions marked, letting him select sound FX while he was accepting input and processing on the other instance, and it worked pretty well, but it's kludgy.
I'm certain there are some radio software packages available, I'm just not aware of who makes them or what the majority of them do.
Either way, latency is the main problem, which is why hardware will do this best.

Thanks alot for your reply. Can anyone recommend a piece of hardware then? I would say the most important feature would be noise reduction. At the moment I am cleaning all the audio up in Adobe Audition which works really well but I was just wondering if there was something that could eliminate this process and save a bit of time.

Thanks

You may want to think about whether any time savings are really worth it in the end. Post really is the best place to do any signal processing on your audio with the exception of applying a limiter to prevent clipping when recording high levels. There you can make your creative decisions at your leisure and can try different options. If you process in real time as you record, you're committed and there's no stepping back if it turns out your choices don't work well in your final production.

I am beginning to realise this. I've managed to tweak the sound quite alot now and the quality of the audio is sounding good. Anything i need to do I'll do in post.

thx