A von Neumann machine is any device that is capable of creating an exact copy of itself given nothing but the necessary raw materials. Create one of these that subsists almost entirely on iron, magnesium, aluminum and silicon, the major elements found in Earth's mantle and core. It doesn't matter how big it is as long as it can reproduce itself exactly in any period of time. Release it into the ground under the Earth's crust and allow it to fend for itself. Watch and wait as it creates a second von Neumann machine, then they create two more, then they create four more. As the population of machines doubles repeatedly, the planet Earth will, terrifyingly soon, be entirely eaten up and turned into a swarm of potentially sextillions of machines. Technically your objective would now be complete - no more Earth - but if you want to be thorough then you can command your VNMs to hurl themselves, along with any remaining trace elements, into the Sun

You will need a light bulb for this method. This is a fun one. Contemporary scientific theories tell us that what we may see as vacuum is only vacuum on average, and actually thriving with vast amounts of particles and antiparticles constantly appearing and then annihilating each other. It also suggests that the volume of space enclosed by a light bulb contains enough vacuum energy to boil every ocean in the world. Therefore, vacuum energy could prove to be the most abundant energy source of any kind. Which is where you come in. All you need to do is figure out how to extract this energy and harness it in some kind of power plant - this can easily be done without arousing too much suspicion - then surreptitiously allow the reaction to run out of control. The resulting release of energy would easily be enough to annihilate all of planet Earth and probably the Sun too.

For this you will need: a big heavy rock, something with a bit of a swing to it... perhaps Mars. Essentially, anything can be destroyed if you hit it hard enough. ANYTHING. The concept is simple: find a really, really big asteroid or planet, accelerate it up to some dazzling speed, and smash it into Earth, preferably head-on but whatever you can manage. The result: an absolutely spectacular collision, resulting hopefully in Earth (and, most likely, our "cue ball" too) being pulverized out of existence - smashed into any number of large pieces which if the collision is hard enough should have enough energy to overcome their mutual gravity and drift away forever, never to coagulate back into a planet again. A 10,000,000,000,000-tonne asteroid at 90% of light speed would do the trick.

For this you need a powerful mass driver, or ideally lots of them; ready access to roughly 2*10^32J. Basically, what we're going to do here is dig up the Earth, a big chunk at a time, and boost the whole lot of it into orbit. Yes. All six sextillion tons of it. A mass driver is a sort of oversized electromagnetic railgun, which was once proposed as a way of getting mined materials back from the Moon to Earth - basically, you just load it into the driver and fire it upwards in roughly the right direction. We'd use a particularly powerful model - big enough to hit escape velocity of 11 kilometers per second even after atmospheric considerations - and launch it all into the Sun or randomly into space. Alternate methods for boosting the material into space include loading the extracted material into space shuttles or taking it up via space elevator. All these methods, however, require a - let me emphasize this - titanic quantity of energy to carry out.

Hijack control of the Relativistic Heavy Ion Collider in Brookhaven National Laboratory, Long Island, New York. Use the RHIC to create and maintain a stable strangelet. Keep it stable for as long as it takes to absorb the entire Earth into a mass of strange quarks. Keeping the strangelet stable is incredibly difficult once it has absorbed the stabilizing machinery, but creative solutions may be possible. A while back, there was some media hoo-hah about the possibility of this actually happening at the RHIC, but in actuality the chances of a stable strangelet forming are pretty much zero.

Total existence failure (TEF) is the hypothetical event of an object suddenly and spontaneously disappearing in a quantum anomaly. The phrase originates from the book Life, the Universe and Everything by Douglas Adams (part of the Hitchhiker's Guide to the Galaxy series), with his tale of the fate of the Starship Titanic. This method is one for the lazy villains out there, as it does not require an input apart from waiting and patience. This is the most least likely scenario to occur, as the probability of it happening is less than a Googleplex to one.

Hurl the Earth into the Sun. Sending Earth on a collision course with the Sun is not as easy as one might think; even though you don't actually have to literally hit the Sun (send the Earth near enough to the Sun (within the Roche limit), and tidal forces will tear it apart), it's surprisingly easy to end up with Earth in a loopy elliptical orbit which merely roasts it for four months in every eight. But careful planning can avoid this. This is impossible at our current technological level, but will be possible one day, I'm certain. In the meantime, may happen by freak accident if something comes out of nowhere and randomly knocks Earth in precisely the right direction. Earth's final resting place: a small globule of vaporized iron sinking slowly into the heart of the Sun.

For this you will need a microscopic black hole. Note that black holes are not eternal, they evaporate due to Hawking radiation. For your average black hole this takes an unimaginable amount of time, but for really small ones it could happen almost instantaneously, as evaporation time is dependent on mass. Therefore you microscopic black hole must have greater than a certain threshold mass, roughly equal to the mass of Mount Everest. Creating a microscopic black hole is tricky, since one needs a reasonable amount of neutronium, but may possibly be achievable by jamming large numbers of atomic nuclei together until they stick. Simply place your black hole on the surface of the Earth and wait. Black holes are of such high density that they pass through ordinary matter like a stone through the air. The black hole will plummet through the ground, eating its way to the center of the Earth and all the way through to the other side: then, it'll oscillate back, over and over like a matter-abso

This method involves detonating a bomb so big that it blasts the Earth to pieces. You will need 2,500,000,000,000 tons of antimatter to do this. Antimatter - the most explosive substance possible - can be manufactured in small quantities using any large particle accelerator, but this will take some considerable time to produce the required amounts. If you can create the appropriate machinery, it may be possible - and much easier - simply to "flip" 2.5 trillion tons of matter through a fourth dimension, turning it all to antimatter at once. This is assuming zero energy loss to heat and radiation, which is unlikely to be the case in reality: You'll probably need to up the dose by at least a factor of ten. Once you've generated your antimatter, probably in space, just launch it en masse towards Earth. The resulting release of energy (obeying Einstein's famous mass-energy equation, E=mc^2) should be sufficient to split the Earth into a thousand pieces.

The nearest black hole to our planet is 1600 light years from Earth in the direction of Sagittarius, orbiting V4641. After locating your black hole, you need get it and the Earth together. This is likely to be the most time-consuming part of this plan. There are two methods, moving Earth or moving the black hole, though for best results you'd most likely move both at once. I do not expect the necessary technology to be available until AD 3000, and add at least 800 years for travel time. (That's in an external observer's frame of reference and assuming you move both the Earth and the black hole at the same time.)