Aragorn dies and then she lives her children (multiple children..not just one son that looks very much like a little girl!) and wanders middle earth (because she's not yet tired of living) and ends up dying in lothlorien where elves no longer are. It's very sad.

And with Eowyn..that was great. And I was very happy that they had Merry stabbing him too (though..what about the Black Breath and the hands of healing of the king?). If you read the appendix at the end of Return of the King it explains the whole thing behind "no man can kill me" because when Glorfindel first went up against the Witch King he made the statement about he could forsee the end of him and it was not by a man's hand (and since Merry isn't a man exactly he could have a part in it)