The title of this blog entry is the search term I entered in Google. The range of responses is quite interesting. Some highlights, in order of their appearance in Google's SEO:

• "Photography contests are a great way to find out if your images are up to scratch. By participating in these competitions, you can win big—either cash prizes, camera equipment, or having your work exhibited. You might not win any money. But posting your images on the competition’s website has a lot of benefits." But it goes on to say "ExpertPhotography is supported by readers. Product links on ExpertPhotography are referral links. If you use one of these and buy something, we make a little bit of money." So, a biased source.
• "It depends.... Photography contests typically don’t offer you any detailed feedback on your images, other than a pass/fail grade — you either win or you don’t. So, contests are not an effective way to evaluate your skills. But they can be fun. And most of us got into photography because we enjoy it. So, if you enjoy entering contests, then of course there’s nothing wrong with doing so.... Above all, do what you feel like doing. Photography is supposed to be fun. Win or lose, your images are your images, and if you like them, and you enjoyed making them, you’ve already won." This page also has a great summary of the difference between "contest" and "exhibitions," including those sponsored by the Photographic Society of America, and why the latter are so valuable.
• "Photo contests are one of the most controversial areas of photo sharing, and not without good reason. Many online photo contests amount to little more than a rights grab with “exposure” as your prize.... I saw a small spike in visitors to my web page for a couple of days and I gained a few facebook followers. I have not booked a single session or even gained a subscriber to my email list as a result of this usage that put my work in front of millions of viewers.... Exposure is fun and it's worthwhile if it's for a cause you believe in, but it is rarely worth much beyond that, so don't fool yourself. [But] if a reputable contest is offering a prize that you covet, for an entry fee that you are comfortable with, then by all means, you should enter any photo you feel has a remote possibility of winning.... Photo contests can be a great way to get valuable feedback and see how your photos rank amongst a group of your peers. Sometimes, you may even win cool prizes, just make sure you're not selling the cow for a handful of magic beans."
• "Are photography contests actually worth it? Our answer in short is yes. Photo contests aren’t about vanity or bragging rights—well maybe a little. But mostly they’re a smart business decision that puts you in front of a new audience, motivates you to evaluate your work, and gives your SEO a boost.... With a contest winner badge on your website, you automatically set yourself apart from other photographers. Winning photography contests adds credibility to you, your images, and your website. It’s an extra added bonus that’ll help transform website viewers into loyal customers.... Submitting to contests presents the perfect opportunity to do a deep evaluation of your work.... So no, we don’t think that winning a photo contest makes you a better photographer, but the process of evaluating your work on a regular basis will.... Getting featured in a popular photo contest gives you great SEO juice. Your Google rankings will increase when credible sites are linking to you."
• "Competitions offer a seemingly quick route to recognition and success. The thing is, though, I do not know of a single photographer who has landed a client because they have won awards, nor have I ever had a client ask me to show them my awards resume. Clients generally only care about the images you produce and if you can provide them with a satisfactory professional experience. And so, before you expend effort and spend your money on entering a competition, be sure you are doing it for the right reasons. If you want to enter them for personal gratification, by all means, go for it, but if you are trying to increase your professional standing, that money and effort are probably best spent elsewhere, like improving your craft."
• "A lot can happen during a photo contest process (from judging to the exhibition), and becoming more aware of what you’re good at and where you need improvement will help you develop your photography career.... Although it’s essential to stick with styles or subjects that you know well, shooting for contests often forces you to try something new and explore different creative possibilities. This type of exposure can push you outside your comfort zone and help you develop new interests, and make you a better photographer overall.... If you want to enter a photography competition with an entry fee, you should keep in mind that you are paying to get professionals in the field to look at your work and give an impartial judgment.... Check the reputation of the brand organizing the contest. The sponsors, the qualifications of the judges, how well-known the contest organizers are, and how often the competition is held. Check out their website to see reviews and comments. You can also look up the previous winners and how they have advanced in their careers after winning.... The Sony World Photography Awards: is one of the most prestigious photography awards.... Some other well-known photography competitions are the IPA or International Photography Awards, the Monovisions Photography Awards, the National Geographic Photo Contest, and the Pulitzer Prize for Photography."
• "That competitive edge is a really good way of driving your photography on by that extra few percent.... In the same way that a themed contest can give you direction, it can also push you out of your comfort zone.... Having a winning entry, be that the overall winner or a top ten photo gives your photography validation. There is nothing that beats this when it comes to things like growing your photography business. The ability to call yourself a prize-winning photographer can go a long way.... If you’re lucky, you might get direct feedback from the person judging the contest. Those contests that allow comments may also lead to fellow contestants commenting on your work. Getting feedback on what you do is a great way to grow as a photographer."
• "Photo contests are worth it, they help you improve your skills and creativity.... Instead of thinking about the destination - the contest prize - consider your journey to submitting the photographs instead. You'll learn something new, no matter the outcome. This knowledge will lead to better photoshoots and a stronger creative intuition."
• "I have two major issues with most of the photo contests I have seen or entered: incentive and transparency. Every photo contest is driven by an “incentive” not necessarily aligned with the photographer’s interest. National Geographic wants to sell magazines, Getty wants to recruit stock photographers, and 500px wants more active users. A city council wants free arts, an event host wants to sell tickets, and many miscellaneous photo contests just want your money. The list goes on and on. The key is: As a photographer you have to examine the incentive that drives a photo contest, and you want to enter only the ones best aligned with your objective and how you want to be evaluated. But, is it possible? Is it possible to know how your works are evaluated in a contest? This brings to my other concern: lack of transparency.... Usually, the only information you get before entering a contest are: prizes, fees, some basic rules, and a big button calling you for action. Sometimes you don’t get to know who the jury are, let alone their qualifications. Other times you don’t get to know the criteria or the process for the evaluation that your works are subject to. It literally feels like money sucked up by a vampire when you “lose” in a photo contest because you get zero response and zero feedback. You don’t even know how you lose! So are photo contests worthwhile competing in? As an amateur photographer, I have to say: Not really. Yes, you do get exposure if you win, but... you are also unlikely to learn much when you lose because of the silent treatment you get. By all means, enter a photo contest if there is a specific goal you want to achieve. Competitions have forced me to examine my skills and made me think (or guess since I receive no feedback) when I lose. It also proves that your works are more than a wow from your friends and family when you do win. Just know what you are getting into and be selective!"

Honorable Mention! So in summary, it sounds like:

• Photo contests can be great exercises to self-evaluate your work. I've certainly found this to be true myself.
• The ideal contests are those that actually provide feedback to participants about their photos. I've found few contests that actually do this. The PSA contests come closest, in that they at least give you a numerical score so you can see quantitatively how good the judges think your images are.
• "Exposure" is great in principle, but seldom makes much of a difference IRL. Best practice might be to put your award banners prominently on your page so people looking to hire you can be impressed by your credentials, and to choose prestigious contests that link back to your website to improve your SEO.
• Contests can be fun and self-affirming, and those are good enough reasons to consider them.
• If you're looking to improve your photography, communities like ViewBug and local Photography Clubs might be better ways to get actual feedback.

Lots to think about.