"The Cold Equations," Tom Godwin
“He didn’t tell you his work was dangerous?”This story reminded me a lot of the TV series Firefly - space as an unexplored frontier, wild and dangerous. It was incredibly moving. I don't want to say too much about it, for fear of spoiling it for others. It's an intense story about a stowaway on a space ship. That's about as broad as I can get, I think. :) Both Carl and Eva recommended this story, so you know it's good.
“Well — yes. He mentioned that, but we didn’t understand. I always thought danger along the frontier was
something that was a lot of fun; an exciting adventure, like in the three-D shows.” A wan smile touched her
face for a moment. “Only it’s not, is it? It’s not the same at all, because when it’s real you can’t go home
after the show is over.”
"The Nine Billion Names of God," Arthur C. Clarke
Another story recommended by Eva. I liked this one because it has a religious aspect to it. I love when faith and science combine and get all muddled. In this (very short) story, a group of monks use a supercomputer to print out every possible combination of letters that could possibly be the true name of God. I especially like this one as I just attended my first Catholic mass this morning and am feeling extra-religiousy today. :)
I will continue adding as I read more stories.