Maybe.
The World Health Organization has released a report [PDF] on the connections between cell phone use and cancer. It concluded that cell phones are a "possible" carcinogen, and there was much out-freaking. But what does this really mean? It does not, it turns out, mean that cell phones definitely or even likely cause cancer. It would be more accurate to say that the report says cell phones do not definitely NOT cause cancer.
The majority of studies still show no causal link between cell phone use and cancer, writes science blogger extraordinaire Ed Yong. All studies have limitations, which is why scientists (but not their PR people) tend to hedge about conclusions until there's an evolution-level preponderance of evidence. (If you see a scientific paper that doesn't recommend more research at the end, you probably shouldn't trust it.) So far, the WHO isn't ruling out the connection, but only one study has demonstrated it with any statistical significance. And importantly, Yong points out, nobody knows exactly how cell phones would go about causing cancer in the first place.
The International Agency for Research into Cancer has five levels of cancer risk. Cell phones are in group 2B, which means there is "limited" evidence from human studies and "less than sufficient" evidence from animal studies that the thing might be a carcinogen in humans. The only lower-risk categories are group 3 (not classifiable, usually because there's not enough data) and group 4 (probably doesn't cause cancer). There's only one entry in group 4.
Other things that have been reported to be linked to cancer include Tylenol, alcohol, insufficient alcohol, baldness, soda, blood pressure medication, breast implants, soy, energy-saving light bulbs, food dyes, sunscreen, antibiotics, long ring fingers, oral sex, and in fact most of the rest of universe.
