Stuart Aken has painstakingly collected and stored in .pdf spreadsheet format a list of writing contests. The list tells a bit about the contest, the length of story required, the amount of money paid to the winner, etcetera.
In the past, I have ignored contests because so many seemed to be a ruse used to sell something. However, there are legitimate organizations that pay a handsome sum, such as Glittertrain, that can help a writer launch a career.
So, in that vein, I am providing a link to Aken’s list. Please use common sense and do your research about the organizations. I am not recommending any of them, but offer the opportunity for you to pursue as you see fit.
https://docs.google.com/file/d/0B709lVx9l5_mSF9HMHNvMWdaSzg/edit?pli=1
or
http://stuartaken.blogspot.com/p/writing-contests.html?spref=tw
Fay Moore: I Want To Be a Writer 