1 Imperial Officer: In order to destroy Alderaan we need to generate 10³⁸ joules of energy with the superlaser.
1 Motti: Yes? And?
2 Imperial Officer: That's more than we can produce, even if we convert the entire mass of the Death Star to energy.
3 Vader: The ability to destroy a planet is insignificant next to the power of the Force.
4 Imperial Officer: Tell that to Prof. Einstein, my lord.

2012-05-03 Rerun commentary: The first Death Star (from A New Hope) is canonically 160 km in diameter. That gives it a volume of 2.14×10¹⁵ m³. It's constructed of metal, but with large amounts of empty space inside. Steel has a density of about 7800 kg/m³. If we assume roughly one eighth of the interior space is structural metal and the remainder is corridors, rooms, and bottomless shafts crossed by walkways with no railings, the average density will be about 1000 kg/m³. This gives it a mass of 2.14×10¹⁸ kg. Multiplying by the speed of light squared (according to Einstein's famous mass-energy equivalence equation E = mc²) gives a total mass-energy of 1.93×10³⁵ J.

Now the density might vary by a factor of 2 or 3, but probably not by as much as a factor of 10, so 10³⁵ joules is a pretty good ballpark estimate of how much energy the Death Star could generate if the entire mass of the Death Star was converted to energy. This would, alas, totally destroy the Death Star in the process.

It's also possible to estimate how much energy would be required to blow up a planet. The bare minimum energy required to pull a planet apart against the force of gravity that is holding it together is called the gravitational binding energy. If you want the gory derivation, it's shown on this Wikipedia page, but the result is U =3GM²/5r, where G is the universal gravitational constant, M is the mass of the planet, and r is the radius of the planet. Alderaan is canonically almost exactly the same size as Earth, so plausibly the same mass as well. Plugging in the numbers gives a gravitational binding energy of 2.24×10³² J.

This is where I've taken a little bit of artistic licence. If you wanted to disrupt Alderaan just enough that the bits would float ever so gently away from one another, this is the amount of energy you'd need to supply. And the Death Star can supply that energy, by converting as little as a thousandth of its entire mass into pure energy. But that's not a planet-shattering kaboom! To make the planet blow up spectacularly, you need to inject much more energy than that. So for the sake of this comic, I assumed an overkill budget of a million times, giving the value of 10³⁸ J quoted. That would be a pretty spectacular explosion. But even an overkill of a thousand times is enough energy to put it beyond the realm of feasibility of the Death Star.

One of course may presume that the Death Star is equipped with some sort of superscience weapon that generates the vast amounts of energy necessary to destroy a planet by some means that our puny Earth physics doesn't understand.

But that's not as much fun to make jokes about.