Eternal recurrence is one thing but IMO it does not have anything in common with reincarnation (in the sense of being reborn). ER, at least how I understand it is the idea that the Universe repeats itself over and over in the same manner, we live the same lives over and over, basically. Where as reincarnation is the belief that if you live a "Good" life you "move up" a notch on some spiritual totem pole being reborn as a person with higher standing on this world for your "Good deeds" in life or some kind of animal (correct me if I'm wrong).
I know that I will die, I think that everything goes black, my body rots and I become fertilizer for the soil that I am buried in, for the earth that gave birth to my species. If you believe we have souls because we are "Alive" then do trees have souls? No one can answer this, we will never know so why worry about it?
Personally I'm not too concerned about what happens when I die, I am more concerned with enjoying my life, today, here and now.
Interesting thread though.
"Inferior organisms succumb and perish or are enslaved. Superior organisms survive, propagate, and possess." - Charles Darwin