Are "broken" planets possible in the real world? In the Star Wars universe, there are mentioned (or rather shown) two planets that had some kind of great explosion in their history. First is Peragus, with its exposed core, that partially exploded during one of early fuel mining operations on the planet; the second is Lola Sayu; the nature of the cataclysm that caused it to break is unknown. Both of the planets are (relatively) stable, even though they are "a bit" cracked.
Are such planets possible in the real world? Or, rather, how long would such a planet be stable, assuming that the explosion that happened on the planet (as I assume nothing else could cause such state) wouldn't push it out of its orbit?
 A: Any object (made of normal planet material) bigger than about 200km radius will form a sphere from self gravity http://arxiv.org/abs/1004.1091
A: The Earth, early in its formation, was hit by a planet the size of Mars, and the impact remelted it (and formed the moon in the process). Mercury was hit by a meteor so big that it broke up the ground on the opposite side of the planet from the impact crater. Do these count?
Several of Jupiter and saturn's moons show evidence of huge impacts, though these are just moons not planets of course.
Unless you hit a planet so hard that you completely vaporise it, the rubble is likely to eventually recondense to reform the planet, or form a new planet depending on your point of view. For planets the size of the Earth the gravity is strong enough to mould the broken bits back into a spherical shape. The planet wouldn't be left as a ball of rubble, and after a few million years, after it's had time to cool down and solidify again, it probably wouldn't look much different from a planet that hadn't been disrupted.
A: My answer is more of a summary of insight that others have presented on a number of questions on Physics.SE.
It is true that all astronomical bodies larger than a certain mass will take on a nearly spherical shape.  The logical process to arrive at this conclusion involves several steps.  I will try to enumerate these with the smallest number of non-trivial steps.


*

*Material strength matters less and less as the scale of your system increases.  A material yield strength (or other definable limit) has units of pressure (like MPa).  When material structure is acting to hold the shape of something against an external force, it offers some some anisotropy in the stress tensor.  As we increase the size of a self-gravitating system, the scale on which this anisotropic component can matter becomes less and less.  Basically on larger scales, even rocky bodies behave more and more like a liquid than a solid.  This does not preclude the existence of complex solid structures and mountains on the surface even though the vast majority the vast majority of the planet behaves mostly like a liquid (see Earth).

*When the material strength matters very little, then a single self-gravitating body will either: attain a shape that is consistent with hydrostatic equilibrium, or it will break up into pieces.  In the presence of angular momentum, the hydrostatic equilibrium shape is non-spherical.

*Most astronomical bodies (but not all) have sufficiently small angular momentum such that they are sphere-like.  If the angular momentum is very high, it will break up into pieces, although practically it probably never forms in such a way to begin with.  There are relatively few bodies spinning below the break-apart threshold but fast enough to be highly non-spherical for reasons that I do not fully understand.  The Kepler space telescope is offering new insights into the variety of planets including those with super-fast rotation and will likely shed new light on the subject.


I have a hard time understanding what the Star Wars pictures are even trying to depict, but I will focus on Lola Sayu since I think I can make out what the picture is showing.  The depiction is akin to an apple with a bite taken out of it.

(Image license CC-BY-SA-3.0, Wikimedia Commons)
Specifically, here are the various reasons such a shape is unphysical for a planet:


*

*The core of the planet is molten, therefore it behaves as a liquid, therefore it assumes a hydrostatic equilibrium shape, and the above shape is not included, QED.  Now, it would be over-generalizing without some qualifiers.  The inner of most rocky planets is molten because of heat left over since its creation and internal heat production.  We can potentially think of a sci-fi scenario where both of these will not be present (just set it for a trillion years in the future).  We defer to the next reason.

*Even with the entire volume being fully solid, there is a separate, distinct, reason that mountains can not be higher than what the material properties will permit, and a planet with 1/4th of the matter blown away as in the case of Lola Sayu, the edges of that crater appear like a mountain to gravity. Limited material strength cannot, against the gravity force, uphold shapes so severely deformed from the hydrostatic condition.


As a final note, the pieces blow off from the planet in the picture are either in orbit, or they will be cleared away within a fairly small amount of time.  Most objects will probably not remain in orbit since they are ejected from the surface, and it will more than likely return to the surface at some point in the future, per:

(Image license CC-BY-SA-3.0, Wikimedia Commons)
Now, obviously you can't tell if something is in orbit from the picture (since a still picture doesn't show movement), but it leaves plenty of unanswered questions.  Where did that mass of the planet go?!  Perhaps it blew away faster than escape velocity.  Either way, I'm pretty sure none of the concerns mentioned here were given consideration in the creation of the artwork.
A: The Earth is the most broken planet in the Solar System.
I'm not saying that the cracks were created by explosions, nor collisions.
A possible explanation: the once intact crust had to crack in the process of cooling. The same explanation is valid to the cracked surface of Mars. 
The hot past climate of Mars is the only able to explain liquid water in it's surface 2Gyr ago.  
 (image from Cartographers Guild -  a forum created by and for map makers and aficionados)
IMO, Mars is a 'broken planet' (inspect google images to be sure)

