There has been a certain amount of panic in the news about data from a US National Toxicology Program study where rats were exposed to cellphone radiation and it has been claimed there was evidence of cancer being caused.
The quick answer is no, it hasn't been proved. There is no good evidence to say that mobile phones aren't safe. Keep using them!
There are far more studies suggesting no link at all - so immediately we have to take any findings with a pinch of salt. As is made clear in Science for Life, a single study is never enough to provide useful guidance as any study can be flawed, and it's important to take in the bigger picture. But also the actual findings of this study aren't as negative as the headlines suggest.
First, the study involved exposing rats (with much less brain shielding than humans) to 9 hours of phone radiation a day for the whole of their lives. That's a lot. No females developed any problems, but 3 per cent of the males developed brain cancer. However, experts have pointed out that the number of cancers was small enough to be a statistical occurrence. What's more, most rats were exposed to higher intensity radio waves than are allowed from a mobile phone - and stranger still, the rats that were exposed to the radio transmissions lived longer than a control group that wasn't exposed.
All this strongly indicates that there is nothing negative to be learned from this trial. See the NIH for details.