If you are writing for a magazine, most will want the word count for a short story at under 5000 words. Some are willing to tolerate up to 7500 or even 10,000 words, but they prefer 5000 words and under.
Anything over 7500 words, I (and others) would categorize as a novelette. Which is, strictly speaking still a short story, just a long one, that can run up to 15,000 or maybe even 20,000 words. That probably isn't what most expect when they ask for a short story.
Same as others. Most magazines consider 7,500+ to be a novelette. More important, once your story gets much over 7,000 words, you'll find it much harder to sell to magazines, if that's the route you plan. As Thinker X said, 5,000 words or less is preferred.
According to the Nebulas, this is the breakdown, and most of the industry agrees. Most of my team's shorts are very short, indeed. Closer to flash fiction, and since we publish them on our blogs we like them that way. Except for one. I once got so into a short story that it ended up being a little over 10k. Firmly in novelette country. Whoops. But the good news is that story has appeared in two anthologies and we're getting ready to write another one. Same world, different topic.