When is this world coming to an end?

It's hard to say, and really, it depends on who you ask. The Mayans say 2012, Christians have been saying it for years.

Any number of cataclysms could befall the Earth; asteroid hit, gamma ray burst from a hypernovae, wiped out by the Nemesis sun (yes it is a real theory), swallowed by a black hole, our galaxy colliding with another, the big crunch (universal expansion reverses itself), the quiet freeze (the universe expanding until all energy dies out), the crumble (the change in cosmological constants and the change of matter itself), etc, etc.

The most reasonably predictable idea of the doom of Earth is, of course, the death of the Sun. It's all to do with physics. A star is a delicate balance between the thermonuclear fusion reactions which threaten to blow the star apart, and the star's gravity which threaten to collapse the object into itself. Once the sun's supply of hydrogen and helium expends itself, the sun will die. But it won't just flicker off, it will expand to the size of a "red giant" swallowing the inner planets and Jupiter. After ingulfing the majority of the solar system, the sun will shrink down into a white dwarf star. This white dwarf is supermassive, but not massive enough to undergo gravitational collapse into a black hole, and thus will burn so extremely hot until it consumes all available energy in its mass and eventually will die out into nothing. The timeline for this happening is, again, about 4 to 5 billion years from now; if we escape every other doom out there.

There's also a number of particularly bizarre end of the universe theories resultant from string theory/brane theory. One of my personal favorites results from the hyperdimensional brane theory. Keep in mind this is so extremely theoretical. In brane theory, which is an 11-dimensional theory, an infinite number of parellel "membranes" or universes, if you will, exist together with variations in events, basic physical laws, and any number of differences between them. Our universe is just one brane among many with appropriate constants and physical laws that allow life and the universe as we know them to exist. Obviously, we can't access these other parallel membranes. The "big rip" would occur when our particular membrane collides with another membrane that's trillionths of a centimeter away from us. This would, in theory, rip our universe to shreds. A collision between membranes like this is supposed to be the precursor to the singularity that caused our own Big Bang. This "Big Rip" is not scheduled to happen for another few trillion years.