To better understand why water appears to have no color we must first understand that, what humans can see is a tiny dot in the electromagnetic spectrum. That narrow range of frequencies (in the vicinity of 400nm-700nm), is the only part of the electromagnetic spectrun visible to the human eye. It includes every color we are able perceive and it is all we are able to see.  

When a material is hit by light (frequency) if any of that frequency absorbed by the material falls into the visible region, it will appear as coloured to us.

If a material absorbs all of the visible spectrum of light, then it appears to us as black. If it doesn't absorb any part of the visible spectrum of light, then it appears as transparent when light is transmitted through it, or white when it's scattered.

Water doesn't have the ability to absorb any part of the visible spectrum of light and thus, it appears to be transparent to us.