The Death Star, I'll grant you, is unbelievably awesome. Order, click, fire—boom, no more Alderaan. It has precisely zero chance of working, however, since a huge laser, no matter how large, could never make a planet explode. It could certainly vaporize a small portion of the surface at a time, and if fired on a major metropolitan area and then wiggled around, it could cause massive damage and death; but you simply can't blow up a planet with a giant laser. Lasers are just very high-energy light; they can heat things, they can melt things, they can even vaporize things; but they can't make solid rock explode. (Nor, by the way, could you fire several laser beams into one another to collimate to one large beam: They would simply go right through each other, because photons are not a self-interacting particle.) Even if we imagine that "superlaser" is a misnomer, because the weapon really fires some sort of high-energy plasma, the amount of energy required to blow up a planet is tremendous. It'd be much easier to simply render the planet's surface uninhabitable (we can do that now with fusion bombs), or even to trigger some sort of gravitational collapse that would turn the planet into a small black hole—see next.

The "red matter" of Star Trek (excellent movie by the way, in my opinion the best Star Trek film yet), on the other hand, could work. If it's hypothetical "strange matter" (no one has seen it, so what the hell? Maybe it's red!), which would be both extremely dense—I'm talking Earths per cubic centimeter—and extremely stable—more stable than ordinary matter; it might also be able to convert ordinary matter on contact into strange matter, in a kind of Ice-Nice doomsday scenario; the result would be a rapid cascade of increasing density, perhaps even to the point where the planet would collapse into a small black hole. In fact, it also makes sense that the little ship would have a lot of the stuff, because it was planning on collapsing a whole supernova into a black hole. (This also makes sense, because while a black hole is bad for the planets around it, a supernova is bad for the entire galaxy around it.) Frankly, it would work even better than the movie, because you wouldn't need to drill to the core of the planet: Just drop it on the surface, and it will perfectly well start the black-hole creating chain reaction. You'd also probably throw the planet off its axis, but if you're destroying it anyway, I doubt you care about such things. One problem in the depiction, by the way: The Swarzschild radius of the Earth (which seems a lot like Vulcan!) is only about 9 millimeters (even Sol's is a few kilometers), so that new black hole's event horizon would be just a tiny speck in the sky, not a big moon-sized sphere.

The only problem, really, is how you store and carry such matter: It's not like plasma, which can be kept in an electromagnetic bottle; indeed, it wouldn't be electrically charged, because it has equal numbers of up (+2/3), down (-1/3) and strange (-1/3) quarks. Its own gravity would stabilize it—hence, it really would be spherical and have the consistency of viscous fluid—but it would also draw in anything nearby, converting it on contact into strange matter. It would interact with the weak force, so maybe you could use that to contain it somehow; but the only way we know of making weak force interactions is with highly-radioactive materials, which poses other problems; also, you'd need to be careful about destabilizing the strange matter into normal matter, or conversely letting the strange matter touch normal matter and convert it on contact.

On the other hand, these are largely high-level engineering problems, which might well be resolved by the 25^th century or whatever (they came from the future as reckoned by people in the 23^rd century!); they aren't fundamental physical problems.

Once again, Star Trek is victorious.