Submitting and Writing Contests

Here are some recent places I came across to submit to:

• Bare Fiction Magazine
  We do not charge a reading fee for submissions to the magazine.
  We read work in the English language all year round, therefore we aim to respond quickly (usually within 28 days). Though we do accept simultaneous submissions, please do keep in mind this time frame when submitting and ensure that you contact us immediately if your work is accepted elsewhere. 
• Narrative Magazine
  WE WELCOME SUBMISSIONS of previously unpublished manuscripts of all lengths, ranging from short short stories to complete book-length works for serialization. Narrative regularly publishes fiction, poetry, and nonfiction, including stories, novels, novel excerpts, novellas, personal essays, humor, sketches, memoirs, literary biographies, commentary, reportage, interviews, and features of interest to readers who take pleasure in storytelling and imaginative prose. We look for quality and originality of language and content. 

A great piece of advice I heard is why not look at submitting to a literary magazine as a kind of contest and submit there. It is full of competition and the reward is great if you succeed at getting published.

Beware

For submitting to contests there is a bit of warning, that some contests (especially ones with an admission fee) are just looking to make money and not help writers at all. Read these warnings.