I would say that my all-time favorite short F&SF story was “Flowers For Algernon”. As with Moris, it is one of the very few times I’ve ever cried while reading a story. Very powerful.
I’ve always thought that the attraction everyone feels for “Nightfall” is the unexpected ending. Asimov has you speculating on all sorts of things, contemplating how you would react in similar circumstances, wondering what all the fuss is, and then throws in the kicker at the end, something you’d never expect that the planet and its stars are in the central region of the galaxy, and the sky is filled with the incredible glory of millions and millions of close stars.
I am quite partial to a short story writer not listed here from the 50s and 60s: Zenna Henderson. Many are partial to “Deluge”, but I much prefer “Captivity” (which, I know, was nominated for a Hugo as a novellette; “Flowers For Algernon” won as a novellette, so sue me
). I read it the first time as a teen and loved it; read it again ten years later and recognized it instantly, and loved it again, and now that I teach, I’ve loved it even more.
“The Long Watch” is actually my favorite Heinlein short story, but that may be influenced by having read about John Ezra Dahlquist in Space Cadet, well before first reading the story.
A particularly funny short story I recall well was “License to Steal”, by Louis Newman. I read it in the 6th Galaxy Reader.
Robert Sheckley wrote many very good short stories. One in particular I loved upon first reading was “Seventh Victim”, which was made into the movie “The Tenth Victim.”
I don’t read much modern short story SF. Frankly, I don’t read much modern SF, period. Tends to be a lot of dreck, and hard to find the really good stuff. I recently re-joined the SFBC, and I’m not seeing anything showing up in the monthly catalogues to change my mind. 