This is actually a question I’d never asked myself until it was asked in the most recent WholesomeBabyFood.com newsletter. They quoted Dr. Sears, the author of many popular baby books, who says that breastfed babies don’t need extra water but formula-fed babies might (read his complete answer here). A certified lactation consultant gives a similar answer here. And Dr. Jay Gordon (he’s often quoted in parenting magazines) agrees – he makes the point that with breastfed babies, it’s the mother who needs extra fluids so that she can make enough milk.
Personally, I can’t recall giving Alex water until I wanted him to learn to use a sippy cup – probably around nine months or so. I think the most telling thing is that their pediatrician has never brought it up, which must mean he doesn’t think Tyler needs extra water. However, Tyler finds Alex’s sippy cups so fascinating that I admit I’ve begun giving him a tiny amount of water in valve-less cups just so he can have his own. I’m pretty sure he gets absolutely no water but it’s a fun activity that keeps him occupied and in one place for at least a few minutes.