What do you all do with your video cameras when you're travelling?
 

Travelling via airplane.

Do you put them in your luggage or do you bring them with you on the plane as carry on stuff, or do you just ups them to where you're going?

Carry on only. UPS isn't a bad idea as long as you have it insured.

Carry on.
That way you can get some cool takeoff, in the air, and landing shots (assuming you've got a window seat).
Still - don't want anyone throwing that around. All electronics (cameras, laptops etc) go carry-on.