I did have a 'booking disappeared' issue once (which was discovered before I arrived at the airport thankfully -when checking in online) but other than that, I often book with third party sites. If it's the same price I might choose the airline, but it's nice sometimes to try to keep all your bookings (with diff airlines etc) under the same roof. Plus some, like Expedia in the UK, give you some small bonuses (like nectar points) for booking there.