Whether participating in photo contests is useful for one’s development as a photographer or not, depends on the photographer, or rather, on what he/she takes away from the contest.
Some contests are judged by a panel of judges, while many online contests (in various Flickr groups, for example, such as Matchpoint Challenge or Flickr’s 100 Best) are adjudicated by the participants themselves. There are even popular sites dedicated to head-to-head photo “duels” (e.g. pixoto). Some sites, e.g. 500px, do not run contests per se, but give photographers bragging rights by ranking their photos and portfolios based on their popularity.
While no competition is objective, I personally value them for the feedback they provide regarding my photos. Incidentally, I found that off-line contests are largely useless from that perspective. Sometimes, the outcomes are surprising, in a sense that some of my personal favourite photos do not resonate with the audience, while others that I do not particularly care about (I would enter them because they fit the theme of a contest, for example) become hugely popular.
It is also interesting to see that different audiences prefer different trends. For example, the 500px community, which consists mostly of photographers, favours more subtle, elaborate post-processing effects than the pixoto community. Pixoto is more representative of a general population, and the preference is given to brighter, more saturated colours and generally images that “pop” more.
Participating in contests gives focus to photography when otherwise might be no external motivation to go out and shoot or creatively process images. Doing this regularly is an important practice for developing one’s skills.
I think that just as it is important for improving my work, receiving criticism helps me develop thick skin regarding the opinion of other people about my work. It may sound counter-intuitive: why invite feedback if what you learn is to ignore it? But it is not ignoring the harsh comments that is valuable, but rather learning not to take them personally. Any artist consciously makes him/herself vulnerable by putting out his/her work out for the World to see and judge. Nevertheless, even though our work is an expression of ourselves (to a degree, this is true of any work, not just photography or art), it does not define ourselves. Developing this concept requires practice, and contests provide such opportunity.