You can't live without it; Water is a huge necessity at Walt Disney World. Some people ship cases of water to their resort ahead of time, others attempt to pack water in their checked luggage only to find their suitcase is soaked upon arrival, and still others just figure they'll buy water bottles at the parks for $3+!!! My best advice for drinking water at the WDW Resort is to buy and take a Filtered Water Bottle! Fill it up anywhere (water fountain, drink station, even your hotel sink) and it will filter the water of impurities and make the water taste great! Toss it in your park bag, and you're all set for the day!
Here's the bottle I use: Rubbermaid 20-Ounce Filtration Personal Bottle -Blue. I went through 3 different types of Filtered Water Bottles before finding and loving this one. You can squeeze and pour water out of the bottle and fill up kids cups very easily. You don't have to sip from a straw like other bottles.
Extra Hint: If you really want to be frugal and skip carrying a bottle of water around, you may go up to any quick service food location in the Disney parks and simply ask for a cup of ice water. They'll give you one for free!