No, not AIRplanes.
Planes, as in - dimensions, worlds, planets.
Right now, all generated worlds are completely independent and can't be interacted with each other - which seems right in the current state of things, as there isn't any logical way for those to interact right now.
However, it is becoming more and more obvious (or not) that at one point, those worlds should be able to have some sort of actual connections with each other.
Might and Magic (1986-2002, not this Dark Messiah and Heroes V-VI bull****) series did it very well - the characters could use spaceships built by the Ancients, a powerful race of space travelers (in M&M, there were both flat and spherical worlds - the flat ones were called ). There were also portals.
I am NOT saying we should use this concept in DF, because there isn't such form of technology.
But WHAT should dwarves and other creatures use to travel between worlds? Magic? Technology (of some strange sort)? Alchemy?
...
So let's just assume that we agreed upon a world-traveling method and now we're using it.
When this happens, your adventurer (if in adventurer mode) or a pack of dwarves (if in dwarf fortress mode) are "removed" from the given world and "saved" in-between them (you could say they're stuck in a limbo). Then the game saves and player has to generate a new world like one would normally do. Only that when it's done, the player (or his squad of dwarves) is flinged into the freshly generated world - somewhere at random. At sea? Over a volcano? In a dark fortress? Or maybe just at a local Mountainhome (or whatever could be left of it, should it be ruined somehow). The game then proceeds as normal (well, kind of, since in Fort mode there wouldn't be an embark screen - your dwarves would be left with what they took, unless we're aiming for a spaceship-travel and there's stuff in it.)
Let's face the possibilities - multi-world civilizations, using worlds as garbage dumps (hippies included), re-civilizing empty worlds, extraterrestrial invasions - FUN is to be had with that!