No, you do not need to create a free account to upload or download files from MediaFire, but we highly recommend that you create one so you'll always be able to manage and share the files and images you upload at any time from any computer just by logging in to your account.

Please see http://support.mediafire.com/index.php?_m=knowledgebase&_a=viewarticle&kbarticleid=26 for more info.