I saw a mention or two about (100%, not mixed) distilled water and just wanted to say that it should NEVER be offered as a water source to a bird or most other animals. Distilled water lacks essential trace minerals and compared to your bird's body is a hypotonic solution. This means it is a double threat: it not only lacks the minerals the bird needs, but will cause minerals to be drawn from the bird's body when it is ingested since they travel from areas of higher concentrations to lower concentrations. There is also a risk of overhydration, though this would be rare unless you bird is already drinking an above average ammount of water. At any rate, if you are using distilled or r/o it is NOT a good ideal unless it is being remineralized. Larger birds may be less threatened by this but for small birds it could be quite devastating.
If you live in a location that uses chlorine, it should evaporate out pretty quickly. If you live in a location with chloramine, however, it will NOT dissapate naturally and can indeed be harmful to your birds depending on the concentration. It may be best to condition it in some way. If you have an (uncontaminated) well, your water is perfectly fine. Tap should always be tested periodically for ammonia, as this is sometimes present particularly in public water supplies.
Basically, know your water and know what's safe. Filtering shouldn't hurt but isn't crucial in most cases. If you use bottled, use spring, not distilled.