Many countries have done studies that seem to indicate short-term exposure to the radiation does not increase risk of cancer.
However, some countries are still uncertain about this, and have requested companies move their towers away from people by at least 100 meters.
An Italian court even acknowledged a "causal" link:
but this has been deeply criticized by public health leaders in places like the US.
For the most part, there hasn't been substantial evidence to say that the towers cause harm to humans more than 100 meters away. Particularly in the case of short-distance exposure, there hasn't been much data because many times base stations are not turned off during maintenance, but the power being sent through to the antennas is cut off, so that the workers do not have to work near live antennas, but a study over around 50 years of people exposed to Radio Frequency (RF) waves indicates no significant negative consequences. In the conclusion the author notes a well-worded disclaimer:
The controversy about cell phones and cancer is likely to
continue either until clear-cut evidence of a hazard is established or
until the public (including politicians, businessmen, lawyers and
journalists) concludes that there is little likelihood of a real and
significant hazard. Perhaps the greatest contribution that scientists
can make to this debate is to help educate the public (and other
scientists) about the uncertain nature of risk assessment, and about the
breadth of disciplines and rigor of analysis that must be brought to
bear if high-quality risk assessment is to be accomplished.
Comes from the following article (same one, two different links):
There have been studies done on animals with respect to RF exposure with possible consequences that you can read about on wikipedia:
but when we're talking about these levels of radiation, you would have to be extremely close for an extended period of time, which is why we haven't yet found results in humans. For the most part, we don't stay close enough to have measurable results and those who do take precautions and avoid long-term exposure.