What causes water to become discolored?

There are a number of reasons why your water could be discolored. In order to find the cause, you first need to look at the water and determine the color, because for each color there is often a different reason.

Cloudy Water
If your water looks cloudy or sort of milky white, it could simply be because of air in your water system. Air in your water isn't harmful at all, and it's easy to tell whether or not that is the cause. Fill up a glass and observe it for about five minutes. If there is air in your water system, the water will gradually turn clear from the bottom up. If it does not become clear or the color bothers you, contact your local water department.

Green Water
There are only about three reasons as to why your water could be green. If you're in a warmer climate, it could be caused by green algae in your water system. This isn't a normal occurrence, however, because most towns and cities keep a close eye on the level of algae growth. If it's gotten to the point where your water is turning green, you need to contact the water department and get it sorted out. On the plus side, it may be gross to have green water, but algae aren't harmful to your health in any way.

If you're in colder climates, there could be copper plumbing corrosion in the veins of your water system. This can be confirmed or denied by a simple water tester kit. If you do have copper corrosion, it's definitely time to switch to a new metal for your plumbing.
Finally, your water may be green because of poor bronze alloys that are going through dezincification. This means that you need to test your water for zinc, and contact your local plumber to help you out.

Brown or Orange Water
Your water may take on a reddish or brown tint if there's too much rust in the water system. Keep in mind that this isn't healthy for you, and you should take care of it through your local plumber immediately. They will be able to easily detect where in the water system rust is occurring and change out the pipes for you.

Blue Water
Having blue water doesn't happen very often, and it needs to be taken care of immediately. Much like having green water, it's almost always due to copper corrosion; however, to the point where it's blue instead of just green means that it's extreme corrosion. Take care of this issue immediately.

Don't stay in the dark about discolored water. If your water is anything but clear, it's always better to get the problem fixed instead of potentially harming yourself by drinking or using it. No matter what color it is, water should almost always be simply translucent, so make sure you get your water checked regularly by a plumber to reduce the chance of dealing with discolored water.