Actually, there is absolutely no evidence at all that cell phones or power lines cause serious health issues. In fact, it’s difficult to prove a negative, but it’s starting to look like exactly the opposite is true. After spending several decades and billions and billions of dollars in research no one has been able to prove anything. With that much effort going into it you’d think that they would have been able to prove something by now.
The reason you think there’s more evidence for it is probably mostly due to the way these things are reported. Once in a while, a scientific study comes along that claims to find something. Sometimes these are obviously biased results (i.e. a study funded by the Cell Phones Are Evil Foundation found, unsurprisingly, that cell phones cause cancer) but for the most part they are legitimate studies conducted by reputable scientists and researchers. Follow-up studies though fail to support the conclusion. But hey, that’s the way science works. That’s why we do follow-up studies and such.
The problem is that the initial study gets front page headlines, where the follow-up study gets buried deep in the news, if it gets published at all. This is because “CELL PHONES KILL” makes a great headline, where “We didn’t find anything” isn’t quite so newsworthy.
Combine this with numerous pages on the internet devoted to the dangers of both cell phones and power lines and it’s easy to see why folks come to the conclusion that there really is something bad going on here. The fact of the matter is that today, despite decades of study, there hasn’t been a single scientific study that has found anything conclusive that has also held up to peer review and follow-up studies.