My favourite short story is Last Contact, by Steven Baxter[1]. It always scared the hell out of me, because it was so... mundane, to the very end.
[1]: https://web.archive.org/web/20080725045740/http://www.solari...
[1]: https://web.archive.org/web/20080725045740/http://www.solari...
Or that one short story about discovering the light of another star was about to reach us… and getting the predictions of its intensity very wrong.