Numerous studies have been done, including those by the federal government. The general conclusions are that no types of cancers or cell changed have been detected under cellphone usage against one's head.
Of course, time well tell in reference to your question, as scientific studies are just that; science.
Even if a low percentage of people did get cancer from cellphones, I would presume it wouldn't happen until late in life, when you'd most likely die of something else anyway. So keep utilizing those night and weekend minutes without any fears!
And as far as health problems; there are people who claim they are "EMF Sensitive", so presumably most of these people will claim it affects their health. However, these people would be better off seeing a psychiatrist to ward of the nausea and sickness they (irrelevantly & factitiously) encounter from exposure to less than 1 watt of transmit power.