Can a penny kill you?

It is possible, though not likely.  If you're walking by the Empire State Building and someone throws a penny off the top, and this penny falls and hits you in the head, it will not kill you, though it will hurt for a while. It won't be moving fast enough to break the skin or crack your skull.  The idea that this could be deadly was busted on a 2003 episode of Myth Busters.

Another way a penny could harm you is if you swallow one.  If it doesn't get lodged somewhere along your digestive track, then it should pass through with no real permanent damage.  The post-1982 mostly-zinc pennies will cause a little more alarm, since the zinc is more easily eroded by stomach acids, and as it becomes more pitted, can easily become lodged in the stomach or intestines.  If you leave it, stomach pains and ulcers are in your future.  But you'll probably go to the hospital long before it actually kills you, so even in the worst case scenario, a visit to the ER will put you back in order.

I'm not sure if there are any other ways that a penny could harm you, unless you're walking crooked because you've got a pocket full of them.  So you should be safe using and spending your pennies.