One genre to skyrocket in popularity in the last five years is Flash Fiction. There is no hard and fast rule on the length limit. Some publications limit the tale to 50 words while others accept as much as 1000.Other names for flash fiction include sudden fiction, microfiction, micro-story, short short, postcard fiction, prosetry and short short story, though distinctions are sometimes drawn between some of these terms; for example, sometimes one-thousand words is considered the cut-off between "flash fiction" and the slightly longer "sudden fiction".
The term "flash fiction" may have originated from a 1992 anthology of that title. As the editors said in their introduction, their definition of a "flash fiction" was a story that would fit on two facing pages of a typical digest-sized literary magazine.
Some of the flash fiction markets will pay. If you are interested in reading some examples or submitting your own for publication:
Flashquake - Flashquake is a quarterly, web-based publication that publishes poetry, flash fiction and flash non-fiction (memoirs, essays, creative non-fiction, and humor). They pay $5 to $25 per submission accepted.
Postcard Shorts – publishes stories of about 250 words. This is as much as you could fit on a postcard. The inspiration for this site comes from Arthur C. Clarke's short story "Quarantine".Tweet the Meat - Tweet the Meat is a Twitter-only, horror/weird/speculative market. Stories must be no more than 140 characters in total. They pay $1 per accepted story.
For more flash fiction markets, you can visit Duotrope and select flash fiction from their drop down menu.
Good luck, and enjoy your flash fiction writing!