I... have doubts that we will become immortal anytime soon. I think it's very possible, even likely, that a mechanism will be created within our lifetime (or that of our children) that removes 'old age' as a method of dying, but I think that a few posters really nailed the chief cause of death that would replace it: boredom.
Specifically, the older you get, the more new things you would need to do to stay interested in life. If society doesn't change fast enough to keep you 'stocked up' on new things to try/new skills to learn, then eventually humanity would reach a point where people either suicide or effectively suicide by trying things that are absolutely foolhardy, because it's the only way to get any sort of rush/feel something.
Basically, maybe the lifespan would end up doubled or more, but a mixture of accidents and suicides would make it so that all but the most commited would be alive to see their 300th.