Efficiency. A singlespeed's chain runs directly from the chainring to the rear sprocket and back. A geared bike's chain snakes around two jockey pulleys to a sprocket that is out of line (left-to-right) from the chainring by much as an inch. Even without the chainline issue the improvement is at least a couple percent, and compared to some of the more crooked chainlines you might run on a multi-geared bike, the difference can be quite a bit more than that. Believe it or not, you can feel the difference. Don't believe me? Find a bike shop that sells a few singlespeed bikes, and pull both a singlespeed and a geared bike off the rack. Now crank the pedals backwards pretty hard and let go. Notice how much longer the pedals spin on the SS bike? That's the difference in efficiency, and it's even more pronounced under load.
Maintenance. No derailleurs to adjust, no jockey pulleys to lubricate, no cables to clean. Most of the maintenance most of us do, other than tires, is on the drivetrain. With a singlespeed all you have to do is take care of your chain. That's IT.
Durability. No rear derailleur to tweak on trail obstacles, no shifters to go bad, no front derailleur to jam, no 11-tooth cogs to wear out early and force you to replace your cassette before its time.
Weight savings. 2 - 3 lbs.
Silence while pedaling. It's just plain less noisy with a SS.
Concentration. You don't have to think about what gear you're in. You don't have to plan your downshift ahead of time when you come to a stop in traffic. It's not like shifting is THAT much of a mental burden, but you'd be surprised how many brainwave cycles singlespeeding frees up for other things. Like paying more attention to traffic. Like paying more attention to your body english, line and speed when you attack that rock garden. Singlespeeding makes you a better technical rider.
Momentum. 1. On a geared bike, when you start losing speed on a climb, you downshift, and you let off the power to do it ... which slows you down even more. On a singlespeed, you stand up and hammer. You get more momentum going up the hill (although it can be exhausing at times!). 2. Because you know climbing can get tough if you bog down too much, you pay a lot more attention to preserving your momentum, and you're less likely to sap away precious momentum with your brakes when you don't need to. 3. Because you carry more momentum going uphill into difficult technical sections, you have an easier time getting through them in the uphill direction. Why is technical terrain harder going uphill than downhill? Speed.
Pride. Let's be honest here. It feels pretty good doing that bad beeotch of a climb in a gear twice as tall as you would have on a geared bike. And people that aren't ordinarily impressed by others' riding are sometimes impressed that you can ride a particular trail AT ALL on a singlespeed.
Elegance. A singlespeed bike has a really nice clean, elegant look to it, with no derailleurs hanging off various places, shifters cluttering up the handlebars, and shift cables running along the tubes.
Cachet. It's a fringe activity. You're a member of a pretty exclusive club if you're a full-time singlespeeder. won't be cool anymore, but I don't think where anywhere near there yet.
Making a statement. There are a lot of people who are fed up with planned obsolescence, Shimano's dominance of componentry, and/or the over-engineering of today's bikes. Some people like making a statement about one of those things, or about noncomformity, stickin' it to the man, or maybe something else they think singlespeeding stands for.
Boredom. Some of the people on this forum are extremely accomplished mountain bikers. They've ridden it all. Singlespeeding is a new challenge.
Makes You Stronger. Mentally and physically.
Also, when you pass gearies on hills you look great, and when they pass you, "Hey, I'm on a SS." Yer covered both ways.
Shifting. No mis-shifting blues. Lots of those, with resulting problems such as chain falling off, having to stop pedaling for a split second when shifting under load at times (loose momentum too), shifting between gears, when you are shifting your thumbs ain't on the handlebar where the really want to be and many more advantages to SS.