Given an infinite amount of time, everything that can happen in the universe, will happen.
More like, "Given infinite alternate universes (forking from possibility, think fractally :3), everything that can happen, does happen."
Some events are time-dependent and can't happen at the same time, so not everything that can happen will.
Also: "self" is an illusion. A useful one, evolutionarily; yes. It's just a feedback loop that we've convinced ourselves must have some tangible presence in or outside the body. Because we're capable of projecting our thoughts further ahead in time than any other creature, we naturally start to fear for the future of our "selves" and wonder what might happen to "it" after we die.
Back to Eternal Recurrence:
I think time is better spent figuring out how to sustain life indefinitely.