Fixed gear and singlespeed rides

I've found that I can use my fixed ride to help with flexibility and training my body to ride in a more aggressive position. I keep the bar position a full inch lower than my other bikes, this works because I tend to use it for shorter distances. If I were doing 40 or 60 mile rides that low my back would be a pretzel -- I know this from experience, I rode my first triathlon bike setup about 2 inches too low for a month and came away from it with a strained SI (sacro-iliac) joint that resulted in 2 months of intense back pain. Riding lower significantly reduces wind/air resistance, which is the primary load on a cyclist moving anything over 12mph.

Fixed and SS bikes are significantly lighter, The various bits that make up the shifting drivetrain on a road bike add up to 4-6 lbs. You'll sure notice this difference when carrying the bike up stairs after a ride. Your cheap 80's vintage road bike weighs in at 25 lbs or more and knocking that down to 20 is quite noticeable. Alternately, if you invest in a modern frameset and components it's not at all hard to put together a single speed bike in the 15-16 lb. range.

Dangers and downsides

The first few days and weeks you ride on a fixie, you will learn that it really doesn't freewheel! I found that even riding conservatively, there were a few situations where it was very hard indeed to unlearn the coasting habit. The most dangerous and hardest to unlearn was my tendency to 'set-up' for a turn by dropping my outside leg, it was hardest to let go of in turns that I hit often in my daily riding.

Because you can't coast on a fixed gear bike, you can't lean as aggressively into turns as on a bike with a freewheel, striking a pedal on the low side in a turn will lift the rear wheel, likely resulting in a low-side crash.

If the chain derails or breaks it can lockup the rear wheel, this will probably result in a serious crash.

Loose pantlegs or shoelaces caught in the chainring of a fixed gear bike present the same hazard.

You have to be extremely careful working on fixed gear bike's drivetrain, never to catch a finger between the chain and a turning sprocket. Because there's no freewheel, the momentum of the wheel will keep it moving and you can lose a finger -- be careful of this!

Going downhill at too high a cadence can result in overuse type injuries to the knees.

On a less serious note, because mile-for-mile you turn more revolutions riding a fixed, chafing can be an issue, I've learned to apply anti-chafe even for short rides.

There are fixie / SS advocates who maintain that riding without multiple gears is more efficient generally. If you ride on challenging hills this is pure BS. Riding up a 10% grade on a fixie is going to reduce all but the very strongest riders to a cadence down in the 30s