To me, this is a sort of general term, whose meaning will change depending on context.
Given no other information, I would tend to think of "long exposure" meaning about a second or more (and it could be a lot more -- hours, and beyond).
That said, I think in certain contexts, even exposures that we'd normally think of as fairly short could be considered "long exposures" -- a 1/100" shutter speed would be a "long exposure" for, say, a shot of a hummingbird through a 400mm lens... there'd be blur, even with a tripod, because the bird's movements are that fast. Usually, though, 1/100" is not something I consider to be a long exposure.
So, how to define it, that would give a general answer? There are a variety of options. Wikipedia says:
Long exposure photography entails
using a long-duration shutter speed to
sharply capture the stationary
elements of images while blurring,
smearing, or obscuring its moving
which I think basically meets what I've said so far, though perhaps makes the 1 second exposure not necessarily count as a long exposure (a sentiment I'd agree with, frankly).
I think what defines it for me is one of two things:
As described above, having motion blur (while, typically though I wouldn't agree always, also having stillness in stationary elements).
Leaving enough time to capture light that what the film or sensor captures looks significantly different from what the human eye can see, unaided. This can happen because of point 1, but it can also happen independently of it -- e.g. in a very dark or very high-contrast scene, you can pick up details that you can't see with your eyes by having a long enough exposure. "long enough" will vary from scene to scene. Looking at a bright sky, trying to capture detail in something that looks silhouetted, it might be 1/100" again; in a dark night, it might be 100"... or any manner of other options.
Hopefully this helps give you a sense of it. For what it's worth, I agree with at least several of the other answers, I just thought I'd put a different perspective on it.