Before I get started let me state the following: I think most "writing contests" on the Internet are frauds. I think people start these "contests" just to rip off writers, especially young writers. Anyone can start one easy enough, I know I could. All I would have to do is dream up a fake "panel of judges", charge a contest entry fee, set up a deadline for entries several months down the road, mock up a web page, state the amount of prize money, then put out repeated calls for entries. Once the contest deadline is reached, I would pick a "winner" using the eenie, meanie, miney, mo system then send them some cash to the “winner” while pocketing the rest. Quality would be irrelevant--I would even bother to let the "panel" read them.
Now, let me state this: Not all writing contests are fraudulent, some are real and on two occasions I did write fiction stories with a contest in mind, and both times I wrote in a new genre. One even went on to publication in the prestigious national magazine the Writer's Journal.
The first story called The Powers of Love is a sword and sorcery story that I entered in a contest held by the now-defunct Writer's Club. Sword and sorcery was the theme for this contest. I knew it was a legitimate contest because at the time I was a Judge for the club (I later went on to be the Contest Coordinator). Of course, I did recuse myself as a Judge for this contest and then I wrote the story which I thought was a pretty good effort. It is a story about a young man, a child, who falls in love with a full-grown woman. Using potions he learned of as a Sorcerer's Apprentice he turned himself into a grown man then professed his love for his intended. The ending has a surprise twist to it that I thought was pretty clever. Anyway, I sent it in under a pseudonym and hoped for the best. Unfortunately, the other Judges didn't think as highly of it as I did so the story did not win any of the prizes we offered. That was fine with me because I enjoyed writing the story and it helped me expand my repertoire of genres.
I entered a second story into a contest held in a place you would not normally think of writing contests. That place was my local county fair along with the pigs, cows, ducks, and other livestock that usually come under the scrutiny of judges in this type of event. I discovered the contest accidentally as I was poring over a fair catalog that was sent to me in the mail. Apparently, this was the first year that writing would be part of the proceedings.
One of the categories was Humor and it just so happened that I had an idea for a story called Myron? The Hero? about a nerdy young mamma's boy who saves one of his friends from a killer almost in spite of his actions. This was the first humorous story I had ever written. I guess it was pretty good because I won the Blue Ribbon! Fresh off the glow of this success, I brashly sent it to Writer's Journal where it received an Honorable Mention and was published in September of 1996.
So go ahead and write for contests if that is what you want to because, as you can see, it can lead to other opportunities, just be sure to thoroughly investigate the contest before you lay your money down.