Blogging contests will only be successful if they are promoted well, have good prizes and have very rigid and well defined rules. As Tom mentioned you'll get extra content for your site but you need to maximise the number of links you will receive too.
For Example: If you are an e-commerce website you could invite bloggers to imagine they have $500 and for them to write a blog post on their site about the products they'd buy with this money and many will link to the products. The prize could then be the $500?
You want to make sure that if the blogger is going to write a guest article for your site that they also write an article on their blog promoting the blogging competition.
You can give out extra prizes based on social measures such as the article that gets the most FB shares, +1's or Tweets that the article receives.