I've heard that it's not wise to give very young babies too much water, because their body's electrolytes can very quickly be thrown out of balance by it (partly because they're just small, and partly because their bodies are still developing the ability to regulate). When my son was just about two months old, we went to Australia for a holiday in the height of summer, and I was worried about him getting dehydrated. I was advised by the doctor to feed more frequently if it appeared that he was thirsty, instead of giving him lots of water (I was breastfeeding).
I think as babies get older you can give them more water, but I'd be looking for the advice of a doctor or nurse about this.