HandBrake is a popular video transcoder. It is open source and available on Windows, macOS, and Ubuntu. It is useful for converting videos from one format to another or reprocessing a video to have different properties such as making it smaller in file size and quality for your mobile device or converting it to a compatible file format. The project has been under active development for years and has reached the milestone of a 1.0 release last week. (Technically, 1.0.1 just came out yesterday too.)
HandBrake is free, easy to use, and very capable for converting videos. It is the most often recommendation I hear for the task. Many people use it to make digital backups of their existing movie collection.
The 1.0 release included many features and improvements. You can read the full list in the announcement article. Along with the new version of the software, a new website for documentation was also launched which makes it easy to get started and use the software properly.