Unicycle touring -- how common?
Unsupported unicycle touring is not very common because it doesn't work very well - you really need to carry more stuff than can comfortably be carried in a backpack while unicycling, which limits the amount of time on the uni, which in turn limits how far you can go. As well, unis are slower than bikes which further limits distances. Towing a trailer kind of defeats the point of a uni, and makes the whole process very difficult. But that's what you need if you want to carry more than a days food and water. That said, people regularly manage 50-60km a day, so it is possible to tour.
These two managed 3500km across Australia, and unicycle forums are where you'll find most of the details.


A unicyclist on a record breaking tour of North and South America has reached British Columbia, after biking more than 22,000 kilometres on one wheel.
Cary Gray of St. Louis, Mo., set off on his epic journey on July 1, 2013 and has already spanned 11 countries: U.S., Canada, Mexico, Belize, Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica, Panama, and Colombia.
In Panama, Gray broke the Guinness World Record for Longest Unicycle Journey,

(via CBC News)

The same guy via Pinterest
Lots of the &quot;unicycle touring&quot; I've been able to find is fully supported - it's one or two people on unicycles, followed by at least one motor vehicle carrying all their gear. This guy rode 15,478km across Australia and also claims to hold the Guinness world record (that site is all about the fundraising effort).
(edit) Also, the legalities can be difficult - in many countries unicycles are technically not allowed on the road, or the rules are bizarre (unicycles are bicycles, so riders must keep at least one hand on the handlebars at all times, for example, or must have two brakes). In Australia and New Zealand, for example, they are sometimes &quot;bicycles&quot; and other times &quot;wheeled recreational devices&quot; which must be ridden on the footpath. I've not seen those rules enforced in either country, but they exist. I suspect if a unicyclist was hit by a car they'd be treated even worse than a cyclist in the same position.