http://qntm.org/?destroy
Has better world-ending scenarios, these for the supervillain among us. This is my fave:
Spoiler!
Existence negated via time travel
You will need: a time machine, heavy rock-moving equipment/explosives.
Method: Using your time machine, travel back in time just over 4,500,000,000 years to shortly (i.e. a few billenia) before the formation of the Earth. What you should find in its place is a young Sun and an accretion disc formed of the dusty/rocky material that will later become our Solar System. Find the patch of material that is likely to condense into the Earth. Now blow up, split apart and otherwise stir up the material so that it never gets a chance to come together and form the Earth. Return forwards in time in several hundred-million-year jumps, repeating the process each time so that no planet of any kind ever forms at roughly 1 AU from the Sun. If you make an error, simply go back in time and try again.
If your time machine is more resilient, or you don't mind dying, you could consider going further back in time. The further you go, the less you need to change the universe to prevent the Earth ever forming. Go back to a few billionths of a second after the universe began and just by being there you'll completely alter the face of the universe to come... although it was pretty hot back then...
Earth's final resting place: When you finally return to the present day, you will be left with a largish asteroid belt where Earth should be. Alternatively, you may find that the matter has been assimilated into the bodies of other planets or the Sun.
Feasibility rating: 1/10. This method relies on fictional technology and has no basis in real events or scientific theory. Time travel in this way is almost certainly impossible.
Comments: My good friend Rob rightly informs me that this course of action does not strictly speaking "destroy" the Earth - there is no actual destruction event in which the Earth goes from existing to not existing. What one ends up with instead is a universe in which the Earth does not and never did exist.
Destroying Rob proved remarkably easy.