I feel the need to make one minor concession to yesterday's sporting spectacle, so I'll begin this Oz post by introducing (or re-introducing, as the case may be) you to a ball-like people from the Ozian island-continent. These are the Roly-Rogues, who originally lived in the staircase-like North Mountains of the Kingdom of Noland. Coincidentally enough, after I'd already decided to write about these people, I came across this, so perhaps I'm not the only one linking the Roly-Rogues with football. In fact, the young King of Noland once refers to them as "footballs." They have round bodies, heads and arms that can be withdrawn into these like turtles, and rubber-like muscles that allow them to bounce around without being injured. After many years of living on a mountaintop, the entire population decided to bounce down to the ground and conquer Nole, the capital city of Noland. They did so fairly easily, and forced the people to wait on them and make soup for them. The royal family of Noland manages to escape the country and seek help from Zixi, the witch-queen of neighboring Ix. Zixi makes a potion that the Lord High General of Noland slips into the soup, putting the Roly-Rogues who eat it to sleep. The people then roll the invaders into a river, and Baum mentions that they were rumored to have taken up residence on a previously uninhabited island, which is shown on James Haff and Dick Martin's map as Roly-Rogues' Island, in the ocean to the north of Noland. In A Viking in Oz, Chris Dulabone picks up with this conclusion, describing how one crafty Roly-Rogue named Lenoil uses an old Viking ship that washed up near the island to trick his fellows into paying him tribute. Eventually, however, they all discover the deception, with the exception of Llewop , the friendliest, dumbest, and hungriest of the Roly-Rogues. Llewop goes on to settle in the Emerald City and play a part in The Magic Tapestry of Oz, in which he gets all the best lines, partially due to how his grammar is so terrible as to be amusingly absurd.
The Roly-Rogues are not the only round inhabitants of the Oz universe. In Giant Horse, the protagonists have a brief encounter with the Round-Abouties, people with round bodies and features who live in a roundhouse on Roundabout Way in the northern Munchkin Country. They spend their time revolving in circles, under the orders of a man known as the ring leader. And in Merry Go Round, a city called Roundabout is integral to the plot. When I was an obnoxiously geeky sixteen-year-old fan (as opposed to now, when I'm an obnoxiously geeky thirty-two-year-old fan), I asked Eloise McGraw if she'd known about the Round-Abouties when writing her book, and she said she hadn't read Giant Horse until later. I suppose this would also explain why the Ozites in Merry Go Round think there are no carousels in Oz, despite the fact that the Round-Abouties had one.  The McGraws' Roundabout is a much better realized community, despite the circular reasoning and conversation of its rather simple-minded inhabitants. These are the Roundheads, presumably named after the anti-royalists in the English Civil War. The city's economy was based on manufacturing round objects and selling them throughout the country, but since the objects they made never wore out, this model eventually ended up in danger of collapse. Roundelay, the Sphere-Seer, had his own underhanded plot to secure a king to make the city prosperous again, but it was Ozma and her friends who actually solved the difficulty. The solution was for the Roundheads to begin selling Pi, their tasty national dish made of prickly pears. She also gave them Sir Greves, a disgraced knight of Halidom who preferred cooking to jousting, to serve as their king.
Finally, I believe I should also mention the Hoopers from Lost King, who were inspired by the then-popular children's game of hoop-rolling. The Hoopers, who live in a park in the midst of a Gillikin forest, are incredibly tall and thin, and progress by rolling into hoops. Their ruler is known as King Rollo the Worst.
 Chris names a lot of his original characters after his fellow Oz authors, usually with their names spelled backwards or otherwise manipulated. I assume Lenoil and Llewop are named after Braided Man author R.K. Lionel and Raggedys/Mister Flint author Ray Powell, respectively.
 The Play Fellows from Grampa also have a merry-go-round, but I don't believe there's any indication that it's motorized.