How can you not love the look of a track bike (forget the person riding it)? The way the lines of the frame are so clean, uninterrupted by levers, cables, braze-ons...it's the bicycle expressed solely as its fundamental components. The experience of riding fixed is different, the connection between rider and machine that much more immediate, the equation between exertion and momentum so much more direct. Getting back on a freewheel bike feels strange, mushy, inefficient.
Riding without a brake should make you more conscious, aware of what you're doing in traffic. You have to think ahead, read where every car on the road is going, where the gaps are opening up and where you'll get boxed in a few seconds down the line. The old argument is that people come to rely on brakes to get them out of trouble, ride less safely because they're confident they can jam on the brakes and stop. That may be true to a point but it doesn't get you out of trouble when someone else is making it dangerous for you. I couriered without a brake for a year, quit because it felt like my knees were slowly separating.
Fixed gears are great for commuters for the same reasons that they're great for couriers - low maintenance because there are so few moving parts that get worn, cheap machines to put a lot of miles on in shitty weather. I think the weight issue is generally nonsense - what's a couple of pounds difference in the weight of the bike making to a rider who weighs ten stone? What's important is that if you live in fairly flat city, you lose very little by having only a single gear and gain substantially in terms of ease and cost of maintenance.
I don't care if a bunch trendy fools want to ride fixed - what it means is that whereas before (as PeterGunn said) fixed gear bikes were expensive and hard to come by, now you can go into any shop and they have replacement cogs and track chains, and you can buy a decent fixed (Bianchi, Surly, Soma or what have you) for less than an entry-level road bike. If you're riding fixed because you like to ride fixed, what do you care about who else rides one?
I ride mostly at weekends now, and I like to head out into the mountains when I do, so yeah, I have a bike with brakes and plenty of low gears. But I also have a fixed, and if I was only riding a few miles a day around a city, that would be all the bike I would want or need.