Very weird but the explanatory section of my question did not appear when posted......

I had inquired when booking air travel, do you typically use a travel agent, book through the airline's website or a third party site like Expedia, or do you contact the airline's reservation desk directly?

In general, I tend to book my flights more often directly from an airline's web page, assuming there is no incredible can't miss deal on a site like travelocity, orbitz or expedia.  The prices seem to be basically the same, but you may miss out on some added mileage bonuses, etc. if you book through an agency vs. the airline web page.

I also do a lot of flying on low cost carriers, and many low cost airlines can only be booked on the airline's web page.

I will always do searches on the bigger agency sites first to compare itineraries and prices, but typically, I don't find the deals to be much better here.

I did, however, recently book one flight through a travel agency where all of the normal sites and the airline site itself were much more expensive than the ultimate price I paid.  Not sure how that works, but it shows that it definitely does pay to shop around before booking!

For whatever reason, on average I find that the airline websites are the cheapest over Expedia, etc.  I know a number of people who will only book through those sites.  I've done Priceline a couple times for airfare, and while the fare was cheap, I ended up with horribly timed layovers (one too long and the other not even close to enough time) making me very wary of using them again. I love Priceline for other things but never had the best of luck with airfare.  And you are right, there is often a loss in mileage when booking through 3rd party sites, which is another downside.