In reply to Andy Long:
When I started climbing (it will be 57 years ago in July) the bowline was the only game in town. It seemed to work well enough for me, so I never changed to anything else.
Recently, it has gotten a bad rep for coming undone. As far as I can tell, this never happens if you are using a backup knot and/or something like the Yosemite finish (I use both), but a bowline without any kind of backup is liable to loosen up and perhaps undo entirely and should not be considered a knot for climbing.
The Yosemite finish/barrel knot backup combination makes the knot stable under ring-loading, but without suitable backups the bowline cannot safely be subjected to ring-loading, as is possible if one belays through the rope loop rather than the harness belay loop.
Once the groundswell of anti-bowline bias got started, people began to assume that a mistied bowline explained all accidents in which the rope came free of the harness without leaving a single figure-eight behind. The fallacy of this assumption is that a distracted climber may never have finished tying their bowline after threading the rope through the harness. This is what happened in John Long's accident, for example, and this type of failure has nothing to do with the bowline as a knot.
If one considers as equivalent the left- and right-handed version of the bowline (the standard bowline vs. the "Dutch Navy" bowline"), then the threading steps involved in tying allow for eight ways the knot could be attempted. Two of these eight ways give you a bowline, four result in something that falls apart in your hands, and two give something that will hang together but is not a bowline and might be dangerous---I don't know if the "wrong" knot has ever been tested.
It is very easy to spot the wrong configuration, because the leader's rope comes out of the "side" of the knot rather than the "top." Given that the other possibilities fall apart instantly, the idea that a wrongly-tied bowline is hard to spot seems to me to be completely wrong.
The knot called the "double bowline" above should probably be called a "rethreaded bowline." The DAV's tests suggest it is the best knot for climbing, but it does put two strands through the tie-in points. If you are using double ropes, that's four strands, at which point things are getting a bit crowded down there. For single-rope tie-ins it is the way to go, but it seems to enjoy a very limited popularity in the U.S. where single ropes are king.
The classical double bowline involves making two loops at the beginning of the knot-tying process rather than one. It is somewhat stronger than a single bowline, but that is irrelevant because climbing ropes never break at the knot anyway. That said, I use a double bowline for lead climbing. The reason is that it has been established that knot-tightening provides some fall-energy absorbtion and I suspect that the extra strands and turns in the double bowline will produce a greater effect.
All in all, it seems to me that the bowline requires just a touch more sophistication on the part of the user than the figure-eight, and for this reason gyms and guide services, who have to worry about liability, are at least advised and in many cases required to use the figure-eight, even if it can be devilishly hard to untie after being loaded. The idea that someone would go so far as to boycott a gym on these grounds strikes me as ludicrous. It just isn't a big deal. Tie whatever knot the gym requires and get on with your day.