cmsplugin_filer_html5video to your
Format support between browsers is a moving target. This plugin provides fields for the three most common formats: MP4 (h.264), WebM, and Ogg Theora. Wikipedia has a table of supported formats for different browsers.
You can upload your videos in some or all supported formats, depending on your needs.
The plugin does not support format conversion (patches welcome!) and does not validate the uploaded files. You might want to educate your CMS staff on the particularities of HTML5 video.