Consider that the impact of a Mars sized protoplanet on the Earth caused the spin to increase to today's 24hr and created the moon.
So to radically increase the spin of a planet, you would need to apply far more energy. Sadly, the sorts of astronomical objects which could provide energy on these scales tend to be the sorts of things which would destroy planets (dwarf stars, neutron stars and black holes). As well, the mechanical stress of spinning so fast will also cause the planet to melt, or if the rotational energy exceeds the gravitational binding energy, to disperse into a rapidly expanding cloud of gravel.
The reason a neutron star spins so rapidly is it has taken the angular momentum of an entire star and shrunken it into a tiny volume of space, much like a figure skater bringing her arms in to speed up her spin. This isn't going to be possible with a rocky planet, and a gas giant planet would need the core to collapse (something which could only happen artificially, such as the monoliths in 2010 turning the metallic hydrogen into neutronium to initiate fusion).
The only way it seems possible to spin up a planet without destroying it would be to somehow artificially spin it up but at a controlled rate. Freeman Dyson (the same guy who developed the idea of the Dyson Sphere and the ORION nuclear pulse drive, among other things) came up with a planetary spin motor, which couples the magnetic field of the planet to an external influence to drive the rotation (sped up or slowed down, depending on what you want):
In real life, the theory of a planetary spin motor was thought up by Freeman Dyson and published in a scientific paper in 1966.
He proposed that a planet could be destroyed by accelerating it's [sic] rotation about its axis until centrifugal forces become greater than its internal cohesive forces. When the planet's period of rotation dropped to about one hour, it would be ripped apart.
In order to achieve the necessary acceleration of the planet's spin, he suggested wrapping it in a metal grid. This grid would be charged by a powerful electric current, creating an electromagnetic force, which would speed up the rotation of the planet.1
↑ Freeman J. Dyson (1966), "The Search for Extraterrestrial Technology", in Perspectives in Modern Physics (Essays in Honor of Hans Bethe), R. E. Marshak (Editor), John Wiley & Sons, New York.
↑ "How to Disassemble a Planet", Space Archaeology, http://spacearchaeology.org/?p=105