I've always got at least one in my carryon -- three (plus an empty sippy cup) if I"m traveling with the family. I carry Brita bottles that have the filter cartridge inside.
I've never been stopped except for one time when DS *SWORE* that he had emptied his out, but had not -- there was about an inch of water in the bottom. Somehow they can tell if there is liquid there.
PS: Just to be clear, you can carry on as much liquid as you like -- you just cannot take liquid through the TSA checkpoint unless it is medical or special feeding supply for a baby.