Phones already have been proven to give cancer. They give off radiation, which is proven, and radiation causes cancer, which is proven. Even if this were not true, phones should still be banned. Texting and driving has killed many people, including my neighbor. Essentially, when you buy a phone, you kill you self and people around you.
The amount of radiation given off by modern cellphones is so small that a person would have to hold the phone to their heads, days at a time, for years on end. It would make much more sense to ban alcohol or tobacco products before we even consider banning cellphones. Furthermore, there are many different types of radiation, just about everything gives off some form of radiation. Eating microwaved food, using a refrigerator, oven, television, anything that has electricity, or even walking in the sunlight. Phones are the least of our worries.
If the close-proximity-to-the-body is required for cancer to come about and it needs very long term exposure, then i'd say no we do not need to ban them. If it is found you are giving cancer to others in the vicinity just by having one in your pocket or on your property, then they need to be banned or improved to restrict the effects to just the user.
If your use is giving others cancer ... Ban that sucker.