The most efficient way to climb is to pick a lower gear and higher cadence and sit towards the back of the saddle. The further back on the saddle you are the better leverage you'll get on the pedals. By doing most of your climbing like this you'll be able to clock a fast time and conserve more energy than someone who clocks the same time but stands up. However just because standing up on the pedals uses more energy doesn't mean it shouldn't be used.
The fastest way to accelerate up a climb is to climb out of the saddle as you can use your body weight to dump more wattage on the pedals. This is less efficient but tactically if you need to bridge to a breakaway or drop some riders this is the way to do it. You just need to time your all out effort out of the saddle so that what you loose in efficiency is made up for in time gained.
This year on Luz Ardiden Lance won the stage by attacking out of the saddle. He had already rode most of the stage's climbs (including the Tourmalet) in the saddle so that he could conserve energy for his attack. When he attacked speed and acceleration were more important than efficiency so he rode out of the saddle to put as much time as possible between himself and his rivals.
If you want to practice climbing steep hills while sitting in the saddle take a mountain bike out on some steep off road hills with loose dirt. You'll find that if you stand up you loose traction on the rear wheel so you end up having to do the whole climb in the saddle. Also because traction is such an issue this type of hill climbing on loose dirt tends to teach you good pedaling style. By this I mean that you end up pedaling smoothly in circles so that you can maintain a constant traction on the dirt.
You mentioned being able to stand up all the way up a hill as being a measure of fitness. For steep hills it certainly pushes you to the limit. For myself I guess I've always liked the challenge of forcing my way up a steep (15%+) hill out of the saddle. I suppose it's fun to be able to say, "Hey, I did that hill in such and such a gear ... so there!"
Here's an interesting question. Most people say that the reason that climbing out of the saddle is harder is because you're shifting you weight around from pedal to pedal and using your upper body. Does this mean then that a pure climber like Richard Virenque or Roberto Heras will find it easier to climb out of the saddle because they are so much lighter? I heard Phil Liggett say that he saw Richard Virenque do an alpine climb in the Tour completely out of the saddle. I can't imagine Cipollini doing the same thing! Does this mean that a pure climber like Virenque can remain relatively efficient while climbing out of the saddle?
Again going back to the Luz Ardiden stage Lance accelerated away standing up but Ullrich stayed seated to chase. Could this reflect the fact the Ullrich is a heavier rider and Lance is that much lighter. i.e. Lance's power to weight ratio is better so he could afford to attack out of the saddle knowing that Ullrich couldn't follow?