Although he will be most remembered for his Beserker stories, I most remember him for a powerful little story called "Birthdays" that packed a lot in its few words. He chose it for his collection "Saberhagen: My Best," and the story has stayed with me since I read it in the early 1980s. I wish I could point people to a copy of the story somewhere, but the collection is out of print, and the story isn't available on the Internet. And it is one of those stories that I truly feel would suffer if I told you anything about it before you had a chance to read it yourself.
But I did have a chance to meet Saberhagen once, at a Philcon I believe. (I think he was Guest of Honor or Principal Speaker.) I told him how "Birthdays" was one of my favorite stories, and he was very glad to hear it. He thought highly of it as well, but very few people ever came up to him to thank him for it. I'm glad I did.