There are some excellent contests, but there are probably more that exist only to turn a profit on entrance fees or run by people nowhere near as qualified to judge as my mom--and she's dead. So how can you tell the good ones from the bad?
First, check out what it takes to submit. Is the entry fee affordable to the typical adult writer? Look for something less than $50. Is the prize money at least 100 times greater than the entry fee? Are there any extra fees for consulting, critique, mailing or delivery beyond the initial submission, editing, photocopying, etc.?
Does the contest promise what no contest can deliver: guaranteed publication from a major house, contracts with agents, internships? (These things can come from doing well, but it's never a sure thing.)
Are the judges people who are employed in the publishing industry and well qualified to judge the writing of others? What are their credentials? Do they seem to check out?
Read the terms and conditions for submission all the way through, no matter how fine the print. What happens if you win? What if you place well but don't win? What rights, if any, do you give up?
Beware any contest which does not have a street address (not just a post office box) and a listed telephone number; which exists only online; which does not share the names of past winners and offer proof they received their prizes; which does not share the names and credentials of judges; which feels 'fishy' and seems too good to be true.
Remember, too, that there's some logic in thinking that if your writing is good enough to do well in a major contest, it's probably good enough to be selling or self-publishing.
Maryn, parroting others to some degree