Here are six systems available for purifying water. Always read the labeling on the product to see what it claims to filter. Steam distillation is the surest method. Water is heated to boiling, and the steam is collected and cooled until it condenses again without the impurities. This method works, but distillers are expensive, slow, and use power.
Carbon filtration is probably the most popular system.
Units containing specially prepared, porous carbon attach under the sink or at the tap. It works fast, removing chlorine, toxic organic molecules, and bad tastes from water. Look for specially designed, solid block and precoat-activated carbon filters, which also effectively reduce heavy metals such as lead and mercury. The downside to carbon filtration is it stops working as soon as the carbon becomes saturated with contaminants. Also, as the carbon collects organic matter, it starts to become a breeding place for bacteria.