To date there is only one option for a totally chemical free pool. That option uses special plants a la mother nature to filter and treat the water. The downsides to this method are algae growth (which no one wants in their pool) and the fact that there are limits to how much you can heat the pool. There are ways to get close to a chemical free pool using Nature2, an ozonator or an ionizer.
Nature2- Nature2 uses minerals to sanitize the water. Using a Nature2 system on your pool can dramatically reduce the amount of chlorine/bromine you use. For a traditional chemically treated swimming pool, chlorine usually needs to be maintained between 1-3 ppm. With a Nature2 system, you only need to maintain a chlorine/bromine residual of 0.5 ppm. The minerals are introduced to the water as it passes through a cartridge (plumbed "in-line"). The cartridge does have a life span and needs to be replaced every 6 months or so. Nature2 offers a variety of different systems for all pool types and does not require any electricity to operate. Remember, Nature2 is designed to lower the amount of chlorine/bromine you need for your pool, it does not replace it.
Ozonators- Ozonators sanitize the water in your plumbing, not in the pool. The reason for this is because ozone is a poisonous gas. Many of the residential ozone systems are designed so that the ozone never reaches the pool (just the pipes) and they also produce a small amount of ozone. The addition of an ozonator allows you to reduce your sanitizer levels to 0.3-0.5 ppm if you are using the ozonator as your primary sanitizer. Ozone does not kill algae the way chlorine/bromine would. An ozonator will need to be plumbed AND wired (120v or 230v). Ozonators do have an electrode that needs to be replaced every so often (approx. 10,000 hours) depending on usage.
Ionizers- Ionizers use a small, harmless electric charge that is passed through copper and silver annodes to purify the water. You still need to maintain a small sanitizer residual (0.5 ppm) in conjunction with the ionizer. You will also need to maintain a copper ion level in the swimming pool as well (.20-.50 ppm). The annode needs to be replaced after approximately 2 seasons (depending on use). Periodically the water will need to be oxidized which can be done with a non-chlorine shock. An ionizer is not intended to replace chlorine/bromine. The addition of one simply allows you to lower the amount you need.