Okay, I admit it. I'm a worthless pedant.
With that out of the way, I would contend that -
1. The proper U.K. term is "fixed-wheel." This is probably the most descriptive and accurate term, but in the U.S., "fixed-gear" has been used for so long that it's probably fine; as someone just pointed out to me, the cog is fixed, and a wheel fixed in place ... well ... you get the idea ...
2. There are several different traditions of riding fixed in the English-speaking world. Ted just described one very nicely - those who really raced on the tracks and knew how to use a glove, and therefore could ride safely without a mechanical brake on either wheel. He pointed out what I would have said - there were fewer automobiles on the roads, and the skills needed to stop were transmitted to new riders. There's the U.K. time-trialing tradition, which involves using a front brake and a lockring-equipped rear wheel, which satisfied British law from, oh, 1930 or so requiring a brake on both wheels. Then there's the U.K. cycling club tradition, which typically involved brakes front and rear with a flip/flop hub.
The "fixie hipster" tradition seems to me to be based on the old U.S. track racing traditions, minus the bike-handling skills.
Admittedly, I live in semi-rural South Carolina. The fact that I recently saw a student HERE riding a deep-dish wheeled, near-non-existent-handlebar-wrapped-in-red-Oury-grips, brakeless fixed-gear bike probably means the fad is over.
I felt sorry for the kid, actually. He was astride the bike, deciding what to do and where to go next, and he was completely divorced from his mount. He finally turned the bike around 180 before mounting, scootering off to a start before trying to find his toe clips. Nobody had taught him how to mount up, how to bring the rear wheel up and the pedals around to the starting position and being able to glide off smoothly. Instead, he was just graceless aboard what should have been the most graceful of bikes. It was all a little like watching a cow swim ...
Russ Fitzgerald Greenwood, SC, USA
(my apologies for the false send of the first part of this message!)