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This question really has a lot of answers depending on who you ask.  There will be many people that look to the technical aspects of the phone.  Does it emit radiation?  Does it emit radio waves that could be harmful to you?

While many studies have been done trying to enforce or dispute those questions, I don't think any of them have been that conclusive.  

It used to be believed that talking on your cell phone while pumping gas could ignite the fumes and cause an explosion or a fire.  In that case then yes, your cellphone could kill you, although I don't believe any instance of that happening has ever been proven.

If someone were texting and talking on the phone and driving and became distracted, that could be a situation where one might say the cell phone killed that person.

Finally, if you were to talk to the relatives of some of the people who died because they fell off a cliff while trying to take a selfie, they might indicate that yes your cell phone could kill you.  Others might argue it was the poor judgement on their part that caused the accident, but that is a more philosophical debate.

Personally, I think if there were significant dangers to using cell phones we would see much more evidence of it given the proliferation of them.

I once saw a episode from Mythbusters where the wanted to proove (or not) the radiation from a cellphone. There was this myth that a gasstation exploded caused by sparks caused by mobile phones. It wasn't true, they tried all kinds of things but nothing happenend. And like you said, there would be many more articles about radiation and the danger if it was really that bad.. :)

I had forgotten about that Mythbusters episode. Very good point!

No one knows yet what the side effects could be using a cell phone. i have often wondered what we could be doing to our bodies especially the new generation who spend all day on their phones.

Have you seen the experiment with the kernel of corn being cooked between the two cell phones using the electro magnetic radio waves. There must be some damage being caused somewhere but the cell phone hasn't been around long enough to see any side effects.  

Yes in many ways

It could be launched at you at high velocity, hit you in the head or even have enough force to crack a rib or stop your heart.

If the screen is cracked you run the risk of getting a cut, which could lead to infection and death

By focusing on your phone while walking across a street you could be hit by an oncoming car, or possibly hit by a driver who is focused on HIS phone and not paying attention to you.

You could receive a text or phone call so shocking or scary or devastating you simply drop dead from the news.,

You could receive your bill, see all your overage and roaming charges and kill yourself.

And this doesn't even take into account when your cellphone AI becomes sentient and ACTUALLY tries to kill you

So as you can see, cell phones are EXTREMELY dangerous and should only be used by professionals in safe monitored settings while under the supervision of a medical staff