UPDATE 2/5/11: Forget it.  I tried it with a nice, clean audio file recorded under optimal conditions, and it was gibberish. They shouldn’t have this on the market.

Adobe Premiere Pro is supposed to now have a Speech Search feature that does automatic transcriptions.  No one claims it’s as good as a human transcriber, but some claim it’s 75% accurate or so.  They advertise it as being for searching audio and video for where certain things are said, but of course it could also be used to do a first pass at transcriptions, IF it is as good as they claim.  I don’t know anyone who has tried it.  I supposedly have access to it — need to see if I can get it working.

Here’s a review:

http://tv.adobe.com/#vi+f1600v1027

And this is from Adobe:

http://tv.adobe.com/watch/digital-video/using-speech-search-to-speed-editing/

I found a blog posting about Get, an add-in for Final Cut Pro that does something similar, but it’s $499 on top of the $800 or so for FCP.