It's highly unlikely that cell phones will give you brain cancer, but that still doesn't mean the little devices are harmless. A few reports of exploding cell phone batteries have circulated around the web in the past couple of years, which is more the result of poor battery usage rather than a design flaw.
"Several phone battery explosions have been registered in the last two years. Most of them were caused by Motorola devices with counterfeit batteries. In the United States at least 83 people were burned from cell phone battery explosions during this period. Most caused by inadequate use of batteries and recharges, according to the Consumer Product Safety Commission (CPSC)."