The Eternal Recurrence is both a parody and a counterexample to the traditional metaphysics and an existential imperative. I want to emphasize the latter more than the former, if only because the other posters seemed to have missed this point.
The doctrine runs like this:
Suppose that there is a fininite number of possibilities which can be instantiated in the world, but an infinite amount of time in which these possibilities can be instantiated. What follows? What follows is that everything happening now has already happened, and will happen over and over and over again an infinite number of times.
As a metaphysical doctrine, it's not very good (I'll get to this after). As an existential imperative, though, it's quite good, because it begs this question: Are you willing to live your life over and over again for all eternity in exactly the same way?
The Gay Science wrote:
What if some day or night a demon were to steal into your loneliest loneliness and say to you: 'This life as you now live it and have lived it you will have to live once again and innumerable times again; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unspeakably small or great in your life must return to you, all in the same succession and sequence - even this spider and this moonlight between the trees, and even this moment and I myself.
The eternal hourglass of existence is turned over again and again, and you with it, speck of dust!' Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: 'You are a god, and never have I heard anything more divine.'
If this thought gained power over you, as you are it would transform and possibly crush you; the question in each and every thing, 'Do you want this again and innumerable times again?' would lie on your actions as the heaviest weight! Or how well disposed would you have to become to yourself and to life to long for nothing more fervently than for this ultimate eternal confirmation and seal?
Nietzsche gives us a litmus test: Is there even a single moment of joy in your life which makes all the boredom, the bull, the suffering etc. worth living over and over again just to get to that one moment of joy?
It's not very good as a metaphysical doctrine...see the Neo-Platonists' classic argument. Suppose that there are an infinite number of days preceding this one. Ok, to arrive to the present day, each particular point preceding this one must be traversed, which is impossible, as per the definition of "infinite." Therefore, we can never arrive to the present day...wait. We have
arrived to the present day! Hm...I guess there aren't an infinite number of days before this one.
Another objection you could use is that it completely ignores the next life. People have lived miserable lives (at least according to worldly ways of thinking) in expectation of the joy of the next.
I'm not sure what a third objection you could use is.