The correct answer to this question is No; water doesn't have a taste. Despite that, there are different types of water available that may taste different. For example, I prefer Aquafina water, but I don't like the taste of Dasani water. Both waters have no traditional taste, but they have different tastes due to the minerals that each water has. The same goes for tap water, which some people may not like due to the way it tastes.
Though every person may have a preference for the type of water they want, water is known for not having a taste because it doesn't activate the receptors of the tongue.
It might be tempting to assume that expert tasters can detect taste even in water when the rest of us cannot. Where it is possible to taste the difference between one water and another, this is not the water tasting but the contaminants present in it.
Much of our tap water is affected by what the water board adds to protect us and it is true that a cup of tea made in Bristol will taste different from the same brand of tea made in Cumbria or Cornwall where the water may contain less additives. Water itself, though, has no taste.
It depends on your sensitivity to taste. Those with a very refined palate may be employed specifically to describe the flavor of different waters. Generally, water is tasteless because it doesn't activate the tongue's taste receptors. It just provides a vehicle for tasty elements that can be added to make a drink.
However, distilled water produces different taste effects for different people. Some might find certain distilled water bitter, others refreshing or bland. In contrast with previous thinking, research has discovered that in mice, the sour receptors are activated by water.