Why are planets different colours?
Short answer: When it comes to colour, planets are no different to any other objects. The colour of a planet is determined by what it's made of.
Long answer: The explanation above is a simplification but it's basically correct. The colour of any object is caused by the way its atoms absorb and reflect different wavelengths of light. If an object absorbs all wavelengths except red, which it reflects, we will see that object as red. The colour of a planet is caused by the most common elements on its surface and in its atmosphere.
Mercury has a surface covered in grey rocks and dust (igneous silicate). There is no atmosphere to interfere with or add to the grey colour.
Venus is a light yellow colour, caused by its thick atmosphere of carbon dioxide with sulphuric acid clouds. The ground colour is almost irrelevant as the atmosphere and clouds are so thick, that's all we can see from space.
Earth has a surface of blue water, green, brown and white land, with white clouds. Together these combine in an overall blue colour.
Mars has a lot of iron oxide (rust) on the ground and floating in the atmosphere as dust. This makes the planet orange-red.
Jupiter has stripes of different colours. These are atmospheric bands, or cloud structures, containing various elements including hydrogen, helium, ice and ammonia crystals.
Saturn has a yellow/orange/brown colour, created by an atmosphere including ammonia, phosphine, water vapor and hydrocarbons.
Uranus has a blue-green colour caused by methane in its atmosphere.
Neptune also has methane in its atmosphere but astronomers aren't sure why it is a deeper blue than Uranus. It appears that there is some unknown component of its atmosphere that makes it this darker colour.
Pluto has an overall orange-brown hue, resulting from different areas of different colours. There are some dark red-brown areas caused by tholins, which are created by charged particles from the Sun interacting with methane and nitrogen. There are also lighter areas of icy material.