The short story is a quintessential part of Science Fiction; in the 1950s/60s it was the main writing form (in the "pulp" magazines). The 70s saw the rise of the mass market paperback which lead to the almost complete demise of SF magazines and short story publication. Thankfully, some editors hung on and, in the early "naughties" there appears to have been a bit of a revival; the remaining magazines seem more stable, and there are several anthologies published every year, usually containing one authors stories. One of my favourite things to occur is the themed anthology, you can even get a collection based around SF dog stories (Sirius, the Dog Star if you're interested). Cats have have been in SF much more for some reason, Anne McCaffrey being a major proponent. Anthologies have been published for many years where the stories are linked, Larry Niven is a good example (e.g. "The Long Arm of Gil Hamilton", the Man-Kzin war books). This may have grown out of the fact that many early novels were published in serial form in magazines, so often sections would (and do!) stand on their own, short stories may grow into novels etc. Niven got to the point of linking virtually all his short works into a "History of Known Space"; other authors have done similar things, Isaac Asimov linked his robot and "Foundation" stories with novels towards the end of his life. Another good example of linked shorts is the Bolo books by Keith Laumer et al.