This article is from the Unicycling FAQ, by Beirne Konarski with numerous contributions by others.
The first and most important reason is that it is fun. It's neat being up on
one wheel, in control. There are other good reasons, though:
Exercise
You are always pedaling a unicycle, so riding is a good workout. Riding
is a low-impact activity, so it is good for people like me with legs
wrecked by jogging.
Transportation
Cruising speed is 8-9 miles an hour on a standard 24" unicycle, fast
enough to use an alternative to a car for local trips. I have commuted
3 miles to work up to 5 days a week, and I use it to run errands. I am
not going to pick on bicycles, but I feel safer commuting with the
unicycle than with a bike. I can ride the unicycle on the sidewalk, out
of the way of traffic, without affecting my speed.
Challenges
You never run out of unicycling challenges. After you learn to ride
forward, you can learn to ride backwards. When you have done that you
can learn to ride one-footed. You can enjoy what you know, but you can
always learn more.
 
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