Flying, Airplane
Flying often describes a euphoric state and/or spirituality (cf. Bird). To fly in dreams sometimes suggests fleeing from something and/or losing contact with reality—a kind of inflation (cf. Fall). The most famous story of a person flying is probably that of Icarus, who flew too high and, as a result, experienced a fatal fall to earth. This, of course, illustrates youthful hubris. Humans do not have wings and are not "meant" to fly (except perhaps in spirit as shamans, and so on); it is not a "natural" state for them, and perhaps it would be wise, like Icarus's father Daedalus, to just land on the ground.
To be inflated means to puff oneself up like a balloon and sail away. Inflation is an avoidance of the harsh realities of limitations.
Fleeing
To fly (even by airplane) can often express "to flee" from something. Note the word "flight," which means both "fleeing" and "flying." Flight carries a negative connotation, but in this context, it can also represent a desire to escape a negative situation in order to reach a better one.
Airplanes
Traveling by airplane can, in some respects, share symbolic content with flying in that one is "up in the blue"; it can also play on one's "high-flying plans." Flying in an airplane is closer to intuition than traveling by train, but it shares the similarity of (probably) not being in control. One simply goes along and, once there, can do little about it.
Traveling by airplane is associated with embarking on a journey toward new goals (the destination is what matters with airplanes, see below). But as much as one is heading toward something, the flight also symbolizes leaving something—perhaps an uninspiring routine. If one dreams of taking a flight but cannot find the right one or cannot depart, it may symbolize being stuck in a situation that one would rather leave behind.
However, traveling by airplane has other significance as well. When traveling by car, one looks out at the landscape and stops at various places; traveling by train, one moves around and perhaps talks to strangers; traveling by a cruise shipo, the journey itself is the experience, and so forth. But characteristic of air travel is that one boards the plane and tries to pass the time until one relatively shortly arrives at their destination (an airport one immediately wants to leave). Thus, traveling by airplane is not an experience in itself, and therefore, the destination is what matters—one does not want to experience the journey; one just wants to arrive (or get away!)—again, in contrast to many other forms of travel. It is not so much a journey as a means to change situations.
Plane Crash
A crashing plane is often a metaphor for a grand plan that fails; like the inflated Icarus, one is forced to fall back to reality.