Now, scientists have investigated this conundrum of everyday physics. Speeding up rather than slowing down can solve the problem, they say.
Alternatively, you can pivot the handle of the suitcase as close to the ground as possible.
French scientists studied a model suitcase on a treadmill to see what goes wrong when a suitcase rocks out of control at high speed. They developed equations to explain why two-wheeled trolleys have a tendency to rock from one wheel to the other.
In cases of unstable bags - after having gone over a bump, for example - they found luggage rocks from side-to-side until it falls over, or it reaches a regular side-to-side swing.
If a regular side-to-side swing develops, going faster results in smaller swings, said the researchers.
"Thus, one should accelerate rather than decelerate to attenuate the amplitude of oscillations," they explained.
"A non-experienced suitcase puller would not react this way. The outcome should not be a dramatic for a suitcase, but it could be troublesome for a trailer towed by a vehicle."
Knotty problems
This leads on to important practical implications of the research, which is published in the journal Royal Society Proceedings A.
"The suitcase is a fun way to tackle the problem but the study would be the same for any trolley with two wheels or blades," Sylvain Courrech du Pont, of Universite Paris-Diderot, who led the study, told BBC News.
"So it will be the same for a caravan or maybe also for airplanes."
In technical terms, the mechanical instability is mainly due to the fact that there is a coupling between the translational motion and the rotational motion of the suitcase.
It comes about because the two wheels are fixed together on a rod.
In April, scientists solved another problem of everyday physics - why shoe laces come undone.
They found the force of a foot striking the ground stretches and then relaxes the knot, while a second force caused by the leg swinging acts on the ends of the laces, like an invisible hand.
This too has practical applications for structures such as DNA.
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