An interesting paper published last month argues that there may be a correlation between mobile phone use and brain tumors.
Any possible negative effects could have dramatic impacts, given the frequency with which phones are used. The paper cites the statistic that there was "a startling 6 billion [cell phone] users worldwide in 2011." That is, the vast majority of the human population has at least used a cell phone.
There has been, in recent years, a variety of papers detailing different potential negative effects of cellphone use ( for example, see here, here, and here).
The effects of prolonged exposure to cellphone radiation is still unknown, but could be very significant.