So, let's run with the idea that transportation in MMOs doesn't need to generate fiero. This still leaves designers with a variety of emotional options.
My two favorites are delight and wonder - the twin joys of beauty and discovery. No matter what the medium (running, teleportation, vehicle-on-rails, etc.), transportation gives designers the perfect opportunity to bring about these emotions in players. It fits because players can be shown things they don't often see, and because the experience doesn't last long. Wonder is a brief emotion, just like transportation in MMOs must be a brief experience. On top of all that, there's a real-world connection: wonder and delight are emotions of fun that you experience while traveling in the real world.
Taking players to places they don't often go is a great way to generate wonder. In WoW, for example, the griffon flies over places that are inaccessible to players, and each different griffon route shows players another piece of Azeroth they would never have otherwise seen. Taking players over these areas encourages them to piece together the world and discover its connectivity. This is a refreshing mental exercise in WoW, since the main play experience has players spending their time in walled-off zones.
Viewing enjoyable artwork generates delight, and moving through an artistic landscape heightens that delight. Artists who know their trade can work with designers to put together amazing transportation paths that elicit delight at every hill, lake, or turn. Vehicles and mounts should be artistically engaging, if not detailed; players are likely to watch their mount or vehicle more than their own avatars during travel. Even in a teleportation situation, the means of teleportation can be made delightful with the skillful use of particle effects, animations, or cut scenes.
Possibly the most important fun emotion related to travel is the visceral pleasure of movement, which can be represented in games by animations.
If 'run' animations for avatars, pets, vehicles, and mounts are crisp, clean, smooth, and exaggerated correctly, it can give players an enjoyable sense of movement. If those animations include some sort of whimsy (like the cat ears that swivel in WoW), all the better. As someone who has studied birds, I'm something of a connoisseur of flight animations. It's more enjoyable to watch strong, flexible wings that pull you through the air with each downstroke than it is to watch stiff wings with plain up-and-down movement. Well-made animations can make earning a mount (or any form of travel) worth the hassle.
So, looking at these emotions (delight, wonder, and pleasure of movement) as the requirements for fun travel, we can evaluate the types of travel found in games.