Short, short stories; micro fiction; nano fiction... whatever you want to call a story that will fit onto a single side of paper, a screen, a matchbook, anywhere - so long as it's small.
I've always thought the point (and there are always exceptions to any literary idea), was that as word count decreases the information density has to increase. You're never going to develop a story or a world or a character as much as a full story, even just a standard short story. So you have to be as evocative as you can. You have to make the reader tell some of the story in their own head, you have to extend the story backwards and beyond the time covered by your few words.
Here's the best example I can give, from Ernest Hemingway (you may have heard of him). The complete story (don't worry, it isn't too long):
For sale: baby shoes, never worn.
Which he called a complete story. It is awesome, so evocative. It tells you so much with so few words.
There's some recent sci-fi attempts here (from known authors, and William Shatner! FTW), and I've seen various others before, but none ever seem to do it for me quite as well as hemingway's original.
I'll give it a go myself at some point soon.
It's worth saying, while we're on the topic, that this is where poetry and prose collide. When you reduce the words available, and increase the meaning-density, your use of language often becomes more creative, and the prose-prose poetry-poetry blur becomes foggier than ever.
Personally I wouldn't say Hemingway's falls into poetry (though I'm sure some people will disagree), but then I think some of the ones on that Wired link above do come close. Especially when people start dropping pronouns and articles.