Cross-posted from here.
Oz seems to have been intentionally created as a place without much reliable transportation. The railroads that were common in Baum's time and the automobiles that were gaining in popularity in his lifetime were nowhere to be seen (well, yet, anyway; more on that later). Even horses are pretty uncommon, so most transportation is by foot, or sometimes on the back of a friendly animal, or by magic. Conveyances do become a bit more common as the series progresses, however, and here are some of the more significant ones:
Ozma's Chariot - Drawn by the Cowardly Lion and Hungry Tiger, the Royal Ruler of Oz rides in this golden vehicle on special occasions. It first appears in Ozma of Oz, and shows up periodically in later books.
Red Wagon - This open wagon, drawn by the Sawhorse, is such an integral part of the series that it seems kind of weird that it doesn't appear until the sixth book in the series, Emerald City. At least, I don't remember it in the first five volumes. In Ozma, the Sawhorse conveys Ozma and Dorothy to Glinda's palace in "a pretty green and pink phaeton."
Glinda's Chariot - I can't quite recall when we first see this aerial chariot, drawn by either swans or storks depending on the book, but it might be Lost Princess. Regardless, it makes a lot of appearances in later books, being the Sorceress' main method of transportation. In Land, Glinda rides to the Emerald City in a palanquin carried by twelve servants, but I think Baum considered the bird-drawn chariot a more appropriate conveyance for the Queen of the Quadlings.
Autodragons - Even as early as Lost Princess, Oz did have some mechanical vehicles. It's just that they were limited to an out-of-the-way area. In the dull city of Thi, these mechanical dragons plod along the streets, pulling chariots that play marching music as they run.
Submarines - Another fairly modern invention that has a place in a small community in Oz, Queen Coo-ee-oh created and controlled these boats with her krumbic witchcraft. Since she's now a diamond swan, the submarines might well not be in use anymore.
Flyaboutabus - Continuing the same basic theme as the last two, this goose-shaped, button-controlled flying vehicle once belonged to the King of Un, an unpleasant island in the sky above Oz. Notta Bit More, Bob Up, and the Cowardly Lion use it to escape from Un, and end up wrecking it on a day star after the Imperial Squawmos smashes all but one of the buttons (the "up" button) with a giant spoon.
Footpath - In the Thompson books, Oz is positively littered with roads and pieces of landscape that carry people throughout the land, usually as a plot device to get characters into strange new places. It's not usually clear exactly how these malicious roads and such come to be (the result of stray magic, perhaps?), but this Footpath with feet is the creation and property of the Wizard of Oz, who must occasionally be as bad a punster as the Woggle-Bug. It has a mind of its own, and the Wizard usually ties it up when not in use, to keep it out of mischief. It will take you wherever you want to go, based on written instructions on a notepad, but not always in the most comfortable way.
Jinrikisha - The main conveyance of the Red Jinn of Ev, this is basically a flying rickshaw. While first mentioned in Jack Pumpkinhead, we don't see it in use until Wishing Horse, and get the most thorough look at it in Yankee. In fact, the latter has Tompy and Yankee riding it to the United States.
Parade Vehicles - In Wishing Horse, characters from all over Oz come to the Emerald City for a celebration in honor of the first Americans to arrive in the country, and many different sorts of vehicles are mentioned. The royal family of the Munchkins rides in a chariot drawn by a blue dragon. The Ragbadians have a "shabby but comfortable open coach." King Ato has an Octagon Chariot drawn by eight horses (despite the fact that the next book, Captain Salt, suggests that Ato could not have been present at this time). The King and Queen of Seebania have a silver coach, but the most interesting to me is Tik-Tok's "mechanical handcar, which he operated himself." There's a vehicle I would have liked to see again, and might end up using myself in a future story.
Wutz's Transit System - Travel through the caverns of the Silver Mountain was accomplished by means of a roller-coaster-like ride that shot up and down through the various parts of the cave kingdom. Since Ozma moves the people's dwellings to the outside of the mountain at the end of Handy Mandy, this system might no longer be in use, but I think it would be interesting to see used elsewhere in Oz.
Ozoplanes - The first (but not the last) Ozian vehicles important enough to have a book named after them, these airplanes were an invention of the Wizard of Oz. They need no runway, as they are launched into their air by means of balloons that fill with a magic gas lighter than helium. Once in the air, the earliest ones (the Ozpril and Oztober) are controlled by means of buttons, but we see one with levers in Wonder City. The planes have many interesting and useful features, including the ability to automatically produce maps of their flight routes. In Ozoplaning, several Ozites use these planes to visit a kingdom in the stratosphere (which is, incidentally, where the title of my journal comes from). Wonder City has Jack Pumpkinhead living in a decommissioned but still functional Ozoplane, which is used to fly to a chocolate star.
Ozcalator - A moving road designed by the Wizard and built by a Quadling named Oz Q. Later. Its only appearance in the series is in Wonder City, in a segment likely not written by John R. Neill himself.
Scalawagons - By 1941, Neill apparently felt that it was time for Oz to have widespread use of automobiles. The book Scalawagons has the Wizard building cars known as, well, Scalawagons, which are at least partially sentient, and run on motor fluid from peli-cans. Copyright law probably prevented later Oz authors from using these vehicles, but there's a good chance they wouldn't have wanted to use them anyway. Not only do the cars make Oz less quaint, but they also make travel in the country too easy, preventing a lot of potential plots. I once wrote a story in which the Wizard decided to un-make the Scalawagons, but the people I told about it didn't seem to like the idea of totally destroying conscious things. So instead, I adopted someone else's idea (I forget who came up with it) of giving the Scalawagons their own island in the Nonestic Ocean instead.
Spoolicle - Neill occasionally drew the Patchwork Girl riding on a bicycle with spool wheels, and his last Oz manuscript, Runaway, finally brings this vehicle into the text. It's Scraps's favorite means of transportation, and the design is credited to Jack Pumpkinhead, who must be smarter in some ways than most folks give him credit for.
Airmobile - The last entry on this list is the only one created by Jack Snow, but it's one of my favorite ideas. It's a sort of car with gravity resistor plates, which allow it to travel through the air with ease. The trouble comes when the Shaggy Man and his companions run into Hightown, a city in the sky above Ev where there is no gravity. The Airmobile won't work there, and pushing it back to an area with gravity results in its being lost in the air.