Motors may be damaged if any of the following occur (may not be a completely exhaustive list)
Any part of the motor reaches a higher temperature than it can tolerate.
The temperature differential between different parts of the motor causes parts to expand or contract out of relative tolerance.
Any part of the motor is subjected to mechanical forces beyond what it can handle.
The magnets in the motor are subjected to stronger magnetic fields than they can handle.
Insulating parts of the motor have higher voltage across them than they can tolerate.
In general, DC motor ratings are based upon whichever of the above would cause failure first under "normal" operating conditions. If for a particular motor one knows which of the above factors was responsible for limiting the specified operating voltage, and knows that particular factor won't apply for some reason (e.g. the limiting factor was #1 but the motor will be operating at an ambient temperature of 4C, and will be operated for short enough intervals that it won't overheat) it may be possible to use the motor at a higher voltage without damage.
It's important to note, however, that even if one could ensure that the factor which had been limiting the voltage wouldn't be a problem, that would only raise the allowable voltage to the point where the next factor would come into play. A motor which is designed for 12V is unlikely to have insulation which is rated for 12,000V even if one could otherwise drive the motor with very short 12,000V pulses without exceeding any of its other ratings.
If the motor's insulation can handle it, driving the motor at 24V half the time and shorting it half the time, switching between the two operations fast enough that the inductance of the motor keeps the current fairly stable, would draw about half as much "average" current from the supply was would driving the motor at 12 volts, and the stress to parts of the motor other than the insulation would be similar to those resulting from 12-volt operation. Some motors would work just fine under such conditions, but others may not. A motor manufacturer should be able to offer guidance as to whether a higher-voltage pulse drive should be usable on any particular device.