On the occasion my kitchen sink's cold water faucet has yellow water. This prompted me to my favorite resource, Google! Here are some common causes of discolored water.
If you have yellow, red, or orange water (like me), you have rust in the water. The variation in color depends on the oxidation of the rust. Rust in the water will not cause health issues.
The rusty water can come from either the city's water main or the pipes in your house. If your issue only arises when using cold water (again, like me), if the color change is sudden, or if the color is discolored at all faucets, then it is a city water main issue. Cities usually do an annual flush of the water main to remove sediment, so the problem might go away on its own. However, if there is low flow in your area, the discolored water can continue.
While the discolored water is not a health threat, it can stain clothes, so don't do laundry while the discoloration is occurring. If you do get a rusty color on clothes, don't use bleach. The chemical reaction will make the stain permanent. All you need to do is rewash your clothes.
If the water is discolored every morning, if the water clears after a few minutes, if the discoloration is at one faucet, or if the discoloration is in your hot water, the issue is in your house plumbing. If the problem is in your home, then you need to replace the rusted pipes. If you have galvanized pipes and choose to replace the corroded pipes with copper, then make sure to connect them properly. If you connect them directly, the copper can cause the galvanized pipes to rust faster.
If you have green-blue water, this is an issue with copper plumbing or brass fittings. If you have this color in your water, it can cause health problems and needs to be immediately remedied. Large amounts of copper in the water can cause gastrointestinal, kidney, and/or liver issues.
If your water is:
BLACK: this could be a mold issue and you should call a plumber to investigate.
PINK: a harmless organism is growing in your water. It causes no health issues.
BLUE: your toilet tank with disinfectant has sprung a leak and is mixing into your water supply. Call a plumber to fix the leak.
GREEN: algae is growing in your water supply.