Contests are a crapshoot.
Now, before all the contest coordinators from RWA chapters put out contract hits on me, let me qualify this and say, "That's totally not a bad thing." Because it isn't. And the reason why it isn't is because writing and submitting for publication is also a crapshoot, and it's a similar crapshoot to the contest crapshoot, so you get crapshoot creds for contests that add a little more experience to your crapshooting efforts in submitting for publication. And I've probably reached the upper limit of the amount of times I'm permitted to use the word "crapshoot" in a single blog post.
Contests have their uses. I used to enter contests when I wanted to test the waters and see if an idea I had (and had pursued out at least a few chapters) would fly. However, that was several years ago, and at the time, I was writing a very specific type of story for a very specific market, which contained a well-documented set of boundaries. I write somewhat more "out of bounds" now, and find that most contests, with the limitations of a single chapter, would not give me accurate feedback on my ideas any longer.
I know of writers who enter contests because of the judge. This is a pretty valuable aspect of many contests, and worth the modest fees. If you have a story that you're aiming to submit to a specific publisher, and want the fast track to the editor's desk, the contest is one way to take a shot at that fast track. The editor has a chance to see your work outside of the slush pile, and in a more timely manner, usually, since most contests have in them a definite results date that's less than a year after you send off your entry, and most NY publishers, uh, don't.
I don't enter writing contests anymore for RWA chapters, primarily because most of them are for unpublished writers and I've been published. However, there are some contests open to writers previously published if they meet certain criteria (f'r'ex, if it's been three years since you've had a contract, or if you're not previously published in a certain subgenre). Most RWA chapter contests are opportunities for unpublished writers to make contacts and earn credits for themselves on the road to publication.
If you are an unpublished writer, contests are a valuable step to take in your road to publication. Especially for folks new to the publishing end of things, or new to the feedback side of writing, contests are a FABULOUS way to get your feet wet without burning any bridges. Contests usually are very specific as to what they will accept in a qualified entry (and the coordinators are usually kind enough to tell you if you failed to meet those criteria and why). Honestly, some contest judges are even more strict on standard submission formatting than editors and agents are. If a new writer submits an entry to a contest that doesn't meet the submission format, you're out postage, and maybe the contest entry fee (although again, some contest coordinators go above and beyond the call of duty and refund you your entry fee, when they really don't have to). If a new writer submits a manuscript to a publisher on scented pink paper with lime green printer ink, thinking something bright and bold will catch the editor's attention, the new writer risks catching attention all right...just not the right kind.
Many writers--even experienced ones, find the submission process so intimidating that they never get around to submitting. Contests can help move a scared writer over the hump of fear--submitting to a contest is a smaller, yet very similar step than submitting to a publisher or agent.
But contests have their downsides, too. A contest final--even a contest win--is no guarantee of publication. For as many Golden Heart finalists/winners who've been offered contracts, there are five times as many for whom that Golden Heart win netted them no luck in the publishing ring.
Contest judges can be arbitrary. In spite of the supreme efforts made by RWA, especially the long-suffering contest coordinators who run these things, there will always be an element of judging that is purely subjective. Contest judges have been known to literally hemmorhage points from an entry for transgressions as small as a sixteenth of an inch margin-difference from the guidelines, to halving an overall contest score simply because the heroine was a redhead and the judge hated redheads.
And contests can provide a writer with a safe haven. Such a safe haven that even when the writer begins to accumulate finals and wins, the lure of the contest win prevents that writer from pursuing true publication options, or even from moving on from a work that's been polished and edited into oblivion, and starting something new.
From the other side, contests are a great fundraiser for an RWA chapter, and some contests have been so consistent with their winners that they've come to carry a certain respect, or to represent a certain quality or characteristic in fiction that they've achieved a small notoriety of their own.
Writing contests can help your career, but use them as you do any tool in your toolbox, and don't let them stand in for something else you may need to pursue more.