In historical stories, the characters have a limited amount of choices. They walk. They might have access to a horse or mule or donkey or pony, which they can either ride or travel in a carriage or cart pulled by that animal. The same choices are available to characters in a fantasy story. The character in a fantasy story might also have access to magical means of transportation: magic carpets, gryphons, pegasi, seven league boots and even travel spells that allow them to disappear and arrive at their destination.
When I was young, my sister and I walked to our elementary school. During the summers we walked or biked everywhere. This is still seems to be the case in the children's and YA books I've read this year.
The college students in town use skateboards as well as bikes and feet to get to class. Will skateboards and inline skates be used in futuristic stories? In Richard Roberts Please Don't Tell My Parents I'm a Supervillain one of the "supervillain" team skates everywhere (in a bear costume). In Sharon Lee and Steve Miller's Sword of Orion (2005), the characters use "slideboards", similar to the hoverboards seen in Back to the Future II (1989). The cartoon series Get Ed also had the characters travel by hoverboard, hoverscooter, a one-wheeled cycle, rocket-powered skates, and jet pack. Another cartoon series, Slugterra, had the characters riding robotic animals resembling wolves and donkeys.
One might think the future will have many ways for characters to get around. Flitters, skimmers, and hovers are terms that come to mind, along with other varieties of flying cars. Some will take big advances in technology, but others might only take a little. And how will public transportation change in the future? Will colony planets revert back to horse-drawn trolleys, or electric or cable? Or (easy solution) will the writer just use the same old terms without detailing the differences if the story doesn't need those details? In Sharon Lee and Steve Miller's Fledgling, distant students travel to class in a bus, but closer students travel by "belt", which is a form of moving walkway.
What other means of transportation have you noticed?