Entering contests is a great way to share your work, and to give yourself a deadline when you want to finish a piece! Contests have deadlines, and rules for entry. Be sure to read the rules completely, and follow the guidelines when you make up your contest submission.
Contest winners are usually published in the publication hosting the contest, and may be paid a prize of money or copies of the magazine for a small literary magazine.
Some magazines charge a fee for submitting to a literary contest. With this fee, you usually receive a subscription to the magazine. This is an accepted and legitimate practice (and one way these small magazines cover their costs to keep publishing).
There are literary contests out there that mask themselves as literary contests, so beware!
For more information:
Facts or Fakes?
How to tell a real contest from a fake.
Preditors and Editors
A listing of reported legitimate and illegitimate publishers and literary agents.
Getting the Scoop on Poetry Contest Scams
A blog helping sci fi and fantasy authors identify writing scams.
Visit the "Contests" section of General and Videos for links to magazines and organizations that hold literary contests in a variety of genres.