If the water is sterile to start with and is in sealed sterile food safe containers it will not go bad.
If the water is in open containers or has living algae or bacteria in it they will grow, especially if there is anything in the water to feed them. Most algae only need basic minerals and sunlight.
So chlorinate your clean water before storing it or sterilize it with heat just like you were canning it.
Another thing that can happen is if the container leaches chemicals into the water, but that should not be a worry if the container is a food safe container.

Water can pick up scents from around it through plastics. After a while it might smell like a musty basement if you are storing it in a musty basement, or like oil if you are storing it near fuel.

Chlorine will eventually gas off even if the water is in a sealed plastic container but it will already have killed any pathogens that might have been in the water or container. That means the water would have to be contaminated from an outside source and so long as the container is still sealed the water will not be contaminated.
Even if the water did get contaminated by algae or bacteria your basic water treatment, chemical or boiling, would make it safe again.

However you will find recommendations all over the place to replace your water supply every 6 months from all sorts of experts. I have not found any of these expert opinions which are backed up by any research.