It's electric. It's stable. Just step on it an lean. It's got big wheels. Compared to a car, it's small and lite. Why not?
Of course, there'd have to be modifications. Gravity is lower, for example. Maybe bigger wheels - there are no roads.
The next step, though, is why not bicycles?
There were no seats in the LEM. To save weight, the shock of touchdown was taken by the standing astronaut's legs.
No seats, but a spare car.
Larry454
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Excellent idea. I used one of those recently on a trail tour in a Florida park. They are simple to use and much lighter than the original lunar vehicle they dragged up there. The only problem I can think of is deep, powdery, dust, which could get a little difficult. But that's difficult in any vehicle. Very thoughtful.
ADDED: The Segway I used was outfitted with "off-road" tires and worked nicely in a trail environment with lots of sand and no pavement. I would not want to try to ride a bicycle in a space suit. Alan Shepard had trouble just swinging a golf club.
ADDED: President Bush's problem was that he was not trained. When you get on one of these things, you have to hold it level until you're on it. Otherwise, it tries to correct as you're getting on. With minimal training before the mission, the astronauts could do this with less risk than the vehicle they already had, which nearly rolled over once.
DLM
Because it doesn't look as cool as a flying car?
I suppose you have a point. I'm not sure about the dynamics of the Segway, I'm sure there would need to be some sort of "dust filtration" modifications that would need to be made, among other things I can't think of right off the bat.
Rastlin
After making some minor modifications. Like different tires, given the rough surface of the Moon. Then sealing up the the motor housing to keep lunar dust out. I don't see why not.
Brant
Sure, if the surface is smooth enough. Everything seems proportional to me.
Personally, I'd like to try using a pogo stick. But the awesome place to go for moon pogo jumping is Deimos. You'd go a mile or two high and stay up for about an hour each jump.
Anonymous
Riding a Segway on the moon could very well restore a person's virginity with the sheer magnitude of the nerdiness involved.