What happens if Mars collides with Earth?

The premise behind the question doesn't hold on any human timescale. Mars orbits the Sun at an average distance of 228 million kilometers (142 million miles), 1.5 astronomical units, outside Earth's orbit. The two paths are separate, the solar system has behaved in an orderly fashion for billions of years, and there's no known mechanism that could put the red planet on a collision course within the next few millennia.

The scenario only appears once orbits are integrated over billions of years, a span long enough for the chaotic nature of the many-body problem to become noticeable. Jacques Laskar and Mickaël Gastineau, of the IMCCE and the Paris Observatory, calculated more than 2,500 trajectories from a realistic solar system model, including general relativity and the Moon's contribution.

Around 1% of the cases ended in a collision between planets, or between a planet and the Sun, within less than 5 billion years. The trigger is Mercury: if its orbit stretches enough, it ends up destabilizing all the inner planets, a process that in one of the solutions begins around 3.4 billion years from now. That produces 29 cases of Mars colliding with Earth, 18 of Venus colliding with Earth, and one of Mercury.

We'd be talking about two bodies of planetary mass, not an asteroid: something on the order of the impact that, according to NASA, roughly 4.5 billion years ago flung molten and vaporized debris from the young Earth into space, which went on to form the Moon — possibly from a single object the size of Mars. But those numbers don't describe a risk; they describe the margin of uncertainty in a calculation spanning billions of years. For any practical purpose, Mars will keep being an orange dot in the sky.