The Webmasters FAQ outlines the nature of acceptable questions for this site: researching available solutions and providing anecdotal advice falls outside the purpose of this StackExchange site, so this type of question would be better-suited to chat or another discussion forum.
That being said, there are a variety of free and open source content management systems, as well as licensed software and paid services, which may meet your requirements.
Some of the most popular content management systems include:
- WordPress (PHP, free and open source) – a blogging platform which has expanded to include many other features – See the wordpress stackexchange if you have any questions.
- Joomla (PHP, free and open source)
- Drupal (PHP, free and open source) – See the drupal stackexchange if you have any questions.
- DotNetNuke (ASP, proprietary or free and open source option)
- MediaWiki (PHP, free and open source) – the software that powers Wikipedia
- Umbraco (MVC.NET, open source)
- DokuWiki (PHP, free and open source) – a simple but powerful wiki software
- Typo3 (PHP, Open Source (GPL)) - powerful for medium and large projects
All of the content management systems listed above are built around the concept of plug-ins which extend the application's functionality—there are many plug-ins, with new plug-ins authored every day.
Sites like The CMS Matrix and WikiMatrix can help you compare CMS's (but is best suited for looking for very particular combinations of requirements).
If you have researched content management systems and available plug-ins but cannot find anything that will meet your needs, you should consult a developer who can build something to your specifications either as a plug-in for an existing content management system or as a stand-alone application.