Condensed results.
Looks like almost everyone books directly with the airline with some booking on Orbitz. Expedia is sometimes used but rarely Travelocity.
This is a small sample from what I would classify as experienced travelers but I wonder if this would hold true for a majority of them? My guess would be that it would.

Now the intriguing question would be what does Expedia, Travelocity, or Orbitz need to do to get your business without losing money?

RESPONDENTS:
Direct Airline site. Kayak for pricing
Direct Airline site, Expedia rarely, Travelocity sometimes, lastminute. Direct Airline for flexible tickets.
Direct Airline site to do the actual purchase. Love the bonus miles. Looking for lowest price.
Expedia
Direct Airline site. Travelocity for the all in one package.
United Airlines and the booking bonus.
Direct websites. Booking bonus and easier to make changes. Alliances and not the cheapest.
Direct Airline site and Expedia for complex itins.
Direct Airline site. Expedia and Orbitz rarely have better fares.
Direct Airline site
Direct Airline site. Expedia and Orbitz for multi airline itins.
Direct Airline site. If cheapest.
Direct Airline site. Orbitz for KE.
Direct Airline site or Orbitz.
200 res with Expedia, 100 with Orbitz and 5 with Travelocity. Mainly go to Direct Airline web sites.
Direct Airline site. Search through Orbitz before booking.
Direct Airline site. Orbitz sometimes. Kayak for pricing
Direct Airline site. Cleaner transaction.
Direct Airline site.