Electronic waves do have an adverse affect on some people. The interference can cause headaches, etc. In general though, I don't think it does particular harm unless you are sensitive to that sort of thing.
Mobiles, can however cause RSI, from repeated texting/pressing buttons.
No, it doesn't worry me, because I may only make 1 call a month. I just use my phone to tell the time, if I'm not wearing a watch at the dinner table! Yesterday a friend had to show me now to ring my husband, while I was out, for him to cancel a dinner reservation, then later when I was getting a lift home, I was trying to ring him from my phone, but I didn't know how too! So as you can see, it's no danger to me! It's lucky we both have a 'no plan' with our phones, so calls may only cost us a few cents or nothing a month