Annihilated by an equivalent quantity of antimatterYou will need: An entire planet Earth made from antimatter
Antimatter - the most explosive substance possible - can be manufactured in small quantities using any large particle accelerator, but this will take preposterous amounts of time to produce the required amounts. If you can create the appropriate machinery, it may be possible to find or scrape together an approximately Earth-sized chunk of rock and simply to "flip" it all through a fourth spacial dimension, turning it all to antimatter at once.
Method: 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=mc2) is equivalent to the amount the Sun outputs in some 89 million years. Alternatively, if your matter-flipping machinery is a little more flexible, turn half the Earth into antimatter (say, the Western Hemisphere) and watch the fireworks.
Earth's final resting place: When matter and antimatter collide, they completely annihilate each other, leaving nothing but energy. All that would be left of Earth is a scintillating flash of light expanding across space forever. This method is one of the most permanent and total on this list, as the very matter which makes up the Earth ceases to exist, making it virtually impossible to even reassemble the planet afterwards.
Feasibility rating: 2/10. It IS possible to create antimatter, so, technically, this method IS possible. But since the proposed matter-to-antimatter flipping machine is probably complete science fiction, we're looking at stupid, stupid amounts of time to pull this off.
Comments: With a significantly smaller amount of antimatter, you can simply blow the Earth up - see later.
Source: This method suggested by Thomas Wootten.
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