You will need: a big heavy rock, something with a bit of a swing to it ... perhaps Mars.

Method: 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 brief analysis of the size of the object required can be found here. Falling at the minimal impact velocity of 11 kilometers per second and assuming zero energy loss to heat and other energy forms, the cue ball would have to have roughly 60 percent of the mass of the Earth. Mars, the next planet out, "weighs" in at about 11 percent of Earth's mass, while Venus, the next planet in and also the nearest to Earth, has about 81 percent. Assuming that we would fire our cue ball into Earth at much greater than 6.8 miles/second, or 11 km/s, (I'm thinking more like 31 mi/s, or 50 km/s), either of these would make great possibilities.

Obviously a smaller rock would do the job, you just need to fire it faster. A 10,000,000,000,000-tonne asteroid at 90 percent of light speed would do just as well. See the Guide to moving Earth for useful information on maneuvering big hunks of rock across interplanetary distances.

Pretty plausible.

Earth's final resting place: a variety of roughly moon-sized chunks of rock, scattered haphazardly across the greater solar system.

Earliest feasible completion date: Ah. Yes. At a billion tons of mass driven out of the Earth's gravity well per second: 189,000,000 years.

Sources: This method arose when Joe Baldwin and I knocked our heads together by accident.

Top 10 Ways to Destroy Earth