brekth has written a short (2,000-word) post-"Metamorphosis" TOS story that, to my mind, pretty much illustrates the whole point of fan fiction. "Flesh of My Flesh" looks at Nancy Hedford's life with The Companion after Zefram Cochrane's death.
In my comment to the author, I said, "This is first-rate storytelling and first-rate science fiction." I don't think that's overstating the case. Recommended reading.