Most likely sendmail or postfix since so many distributions and unix versions ship those as the default MTA. My guess would be sendmail by a narrowing margin... but that's based on what I work with and see in the field not any irrefutable evidence or a good statistical survey.
qmail imo should not be used period. It has been surpassed in speed, functionality, usability, and security (at least once you apply the dozens of patches required to get it to be usable as an mta that meets standards today... i would like to see it come back and be an actively maintained project again, but until then, it really shouldn't be used unless you're using an app that requires qmail... and then I'd argue it's time to find an equivalent app.)
Between sendmail and postfix, I like postfix better. Sendmail is, well, sendmail. You're almost guaranteed compatibility with everything but it has a lackluster security history. Anymore on new deployments I suggest postfix the vast majority of the time. If there is a lot of specialized custom things occurring on the server I often suggest exim (it is by and far the most flexible mta around) and sendmail is always a fair fallback if necessary.
Data1:
http://www.oreillynet.com/lpt/a/6849 (2007, not ancient)
Data2:
http://cr.yp.to/surveys/smtpsoftware6.txt (2001, pretty old)
