HTML5 Video Player: Projekktor
The player supports playlists and can display the videos in full-screen.
It has a control panel which appears on-hover and can be easily customized/themed by editing a single CSS file.
For extending its capabilities, Projekktor comes with a plugin interface.
Having the great features said, we must mention that the player is not perfect yet (in alpha stage).
Considering the inconsistencies between browsers in HTML5 support, browsers may act differently while displaying the player (more details on its website). However, it is under heavy development and new features/fixes are added regularly.
Compatibility: All Major Browsers (with few issues)