From: James R (Avatar)
The planets are in orbit around the sun in the same way as satellites and the moon orbit the Earth. Let's take a satellite in orbit around the Earth as an example. If you simply put the satellite in space above the Earth and let it go, it would fall straight downwards and crash on the Earth's surface. To prevent this happening, satellites are given a "push" in the direction parallel to the Earth's surface. They still fall towards the Earth, but as they fall the Earth's surface (being curved) appears to drop away below them, so that they stay a constant distance from the surface.
It is the same with the planets, but now the Sun pulls the planets "downwards" towards the Sun. The planets do not fall into the Sun because they are travelling fast "horizontally" - fast enough to go around instead of just falling down.
The planets stay in their orbits because there is nothing which acts to change their orbits. The Sun is the major force pulling the planets (by its gravity). The planets do not crash into each other because they orbit at different distances from the Sun.
As for Halley's Comet: the tail is caused by bits of ice and dust being blown off the comet by particles streaming outwards from the Sun. Every time the tail forms, the comet (a "dirty snowball") partially melts and disintegrates.