The fee for contests seems to be its own closet industry. I remember listening to Joyce Carol Oates speak many years ago, and she said that there were no contests that were not fixed. I found that so cynical and depressing coming from someone who obviously would never need a fixed contest. The academic version of this are departments who run "searches," which they are legally bound to do, when they have already picked their candidate.
When I heard Ms. Oates speak, I had just moved from playwriting to fiction, so I thought I would test this out. After carefully checking out the contests to make sure they were legit, I forked out my ten or fifteen dollars and entered some. I won a couple and was happy that the world was not as uniformly corrupt as Ms. Oates implied. After that, I decided never to pay again for a contest unless there was a subscription included; fair is fair. This year, however, I sent my adult novel to a contest and it won and will be published. Still, while my experience is that good things can come from these contests, I don't generally bother with them. I'd rather focus my energy on straight submissions and publication; the literary journals that run most of these contests also accept unsolicited submissions, and many now accept on-line submissions so you don't have fork out for postage either.
If you're going the contest route, it seems wise to analyze the cost/benefit ratio. A legitimate contest where your book might be published seems worthwhile, while a small prize or mere publication in a journal to which you could submit anyway may not be worth the cost, given the odds against you. Obviously, you want to consider the fee relative to the monetary prize.
There are also awards that don't charge, which are usually supported by a larger body such as a university, publisher, or arts council (Check your own state's art council).
Thereadingtub.com has a list of prizes for writers of children's books. There are several web-sites and magazines that list adult awards.
A quick google search turned up many web-sites that focus on exposing scams. Science Fiction and Fantasy Writers of America, SFWA.org, has a good article on the contest industry.
I might add that we are lucky to be in the children's field where there is still vast enthusiasm for great writing and originality. In the adult field, that is not the case. I have many friends who have written beautiful adult books and been told by their agents: "What a masterpiece. But there's no market for it. I can't sell it."
Good luck to all.