Levitation: A means of floating above the earth without using aerodynamic lift or aerostatic buoyancy. Wikipedia has a summary of different types that includes a mention of animal levitation. In Speculative Fiction, levitation might mean magic, such as a flying broom; it could mean anti-gravity, popular in far-future SF; or most pragmatically, it could mean magnetic levitation, popularly called mag-lev. This last is the only one we actually have working examples of, and engineering it requires not just special vehicles, but special rails to run them on, and vast amounts of power.
Tech Level: High. We’re barely getting started in the 21st century. Best fit: Space Opera.
Appeared In: In the case of magical levitation, we can look all the way back to the flying carpets of Arabian Nights. In Science Fiction circles, anti-gravity or null-grav has appeared in everything from Star Wars (I’m thinking of Luke’s speeder) to David Weber’s Military SF.
For Your Plot: Force fields, tractor beams, and artificial gravity exert an irresistible pull on Space Opera. Like faster than light travel, these technologies are as desirable as they are elusive. To write certain types of SF, they are pretty much essential. But please be careful not to give your heroes unlimited powers. Make them struggle.