I'm going to jump into this never-ending debate. First, let me say what I _teach_ and how I explain lift to students. Then I'll say what I _believe_ in.
I teach that lift is primarily produced by the Coanda Effect. Just google "Coanda effect" to learn the details of this principle.
Basically, Coanda effect explains why fluids have a tendency to adhere to a surface, as long as that surface does not curve too sharply. As air flows over the top surface of a wing, it tends to follow that curve. I don't understand why. I just know it does. When the air reaches the back of the wing, it continues downward. Because of Newton's Third Law, this overall downward motion of the air must have an opposite reaction. That reaction is the wing being forced upward. Lift.
To see this effect for yourself, dangle the backside of a spoon against a stream of water from a faucet. As soon as the water touches the spoon, it will be deflected towards the spoon and the spoon will be pulled into the stream of water.
I like the explanation of Coanda effect because it can be used to explain things like stalls. Fluids can only adhere to a curve up to a given "steepness." This explains why almost all wings stall at a 16-20 degree AoA. It also explains accelerated stalls in any flight attitude. It also explains why the density of air affects lift.
I use Bernoulli's Principle to explain wingtip vortices. Once again, I don't believe in the explanations of using a second upside down wing to show how you could say air is flowing through a constricted pipe. I think that's garbage. I also don't believe in any of those explanations of air is moving faster over the top of the wing because it has a larger distance to travel. It does move faster over the top of the wing, but not because of the longer distance. I don't understand why it moves faster--I just know that distance has nothing to do with it.
The bottom line is that there is, indeed, lower pressure on top of the wing. Because of this pressure differential, air "wraps up" around the wingtip from underneath the wing where there is higher pressure. Because the wing is constantly moving, by the time the air rotates from the underside to the top side, the wing has gone past. Hence, spirals are created. Why does this create drag? Because any air flow less than smoothly straight back uses energy. Wasted energy is drag.
That's what I teach.
For what I believe in, I've stopped trying to figure it out. I don't know how lift is produced. I've done a fair amount of reading and research trying to figure it out, and I've come to the conclusion that both the Coanda effect/Newton's Third Law and Bernoulli's Principle don't completely explain lift. From the reading I've done, I've concluded that only advanced math and physics can accurately describe lift. I need to learn more in that area, but haven't had the time. I think Coanda effect and Bernoulli's Principle are just flawed explanations passed on through generations of pilots and flight instructors who don't have a solid understanding of lift themselves (myself included).
Some references for further reading:
http://www.amasci.com/wing/airfoil.html (An EXCELLENT resource for both explanations. This convinced me that math is the only way to accurately explain lift)
http://www.aa.washington.edu/faculty/eberhardt/Lift_AAPT.pdf
http://www.aeronautics.ws/blunder1.html
(These two sites give good support to Coanda)