Reusable water bottles are often made of polycarbonate (also called Lexan). This material leeches a chemical called Bisphenol A (BPA) which has been demonstrated to cause many health problems.
Avoid bottles made of polycarbonate plastic. These bottles are hard transparent plastic (they may be colored) that are usually marked number 7 on the bottom. Some brands of bottles (like Nalgene) have switched to a plastic that does not contain BPA. Other brands continue to contain BPA. Also avoid re-using disposable plastic bottles, which have also been shown to leach chemicals. Plastics marked number 1 are considered to be the safest.
If you would rather avoid plastic altogether, try a stainless steel bottle (like Klean Kanteen) which have not been shown to leech chemicals into water. A glass bottle is the safest choice of all (because glass is totally natural and non-reactive) if you can avoid breaking it.