We understand that many startups are extremely cash-strapped and limited to the low-end of the design market. For these companies, some will consider using design contest websites. However, it's important that every company that considers using a design contest website understand the associated risks so that they can make the best decision for their business and take the appropriate steps to manage the dangers and avoid common problems during the process.
Design contest websites allow companies to post inexpensive logo projects and receive concepts from a large number of designers that are willing to work for free at the prospect that they might be paid if you select their logo as your final design. Why are these designers willing to work for free? The answer is that most of these designers can't find paying work, are located in developing countries, and are relatively inexperienced.
The vast majority of the professional design community is adamantly opposed to design contests. The AIGA "the professional association for design", which has more than 20,000 members, has taken a formal position that outlines the risks to client and designer.
Several other educational/outreach/activist organizations have started in the past few years. These include the NoSpec movement and Spec Watch. Spec Watch is focused on reviewing the projects posted through design contest websites (available publicly through Google) and presenting findings of copyright problems, clip art, unethical practices, and other issues. NoSpec is focused on educating designers and the public to the dangers of working on 'speculative work', which includes the practice of working for free with the hopes to potentially get paid, as in design contests.
Spec Watch does a great job writing about past examples that include copyright violations, plagiarism, use of clip-art, and other concerns. Rather than run through all of the examples here, it's best if you just check out the site.
When working through a design contest site, you have little to no actual interaction with the designers working on your project. Your only communication will be through messages posted on the website. This is a problem because none of the designers will be able to truly understand your business, industry, and project goals without actually speaking with you. You will likely never know your designers name, address, or phone number.
If you ever need to contact your designer again in the future, you may be out of luck. This also creates a very big problem as it relates to copyright ownership and trademark infringement. When working with designers overseas in developing countries, you often have little legal recourse available to you in the event that the designer fails to fulfil their obligations. Designers from some countries will have very little concern for copyright infringement and may will be protected from a local legal system that often does nothing about it.