10. Total existence failure
You will need: nothing
Method: No method. Simply sit back and twiddle your thumbs as, completely by chance, all 200,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 atoms making up the planet Earth suddenly, simultaneously and spontaneously cease to exist. Note: the odds against this actually ever occurring are considerably greater than a googolplex to one. Failing this, some kind of arcane (read: scientifically laughable) probability-manipulation device may be employed.
Utter, utter rubbish.
9. Gobbled up by strangelets
You will need: a stable strangelet
Method: 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.
Earth's final resting place: a huge glob of strange matter.
8. Sucked into a microscopic black hole
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. This is left as an exercise to the reader.
Method: 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-absorbing pendulum. Eventually it will come to rest at the core, having absorbed enough matter to slow it down. Then you just need to wait, while it sits and consumes matter until the whole Earth is gone.
Highly, highly unlikely. But not impossible.
Earth's final resting place: a singularity of almost zero size, which will then proceed to happily orbit the Sun as normal.
Source: "The Dark Side Of The Sun," by Terry Pratchett. It is true that the microscopic black hole idea is an age-old science fiction mainstay which predates Pratchett by a long time, he was my original source for the idea, so that's what I'm putting.