No, that is not possible. You can use oEmbed for some video sources, but for your own video you have to decide what a player you want to use.
That’s exactly what plugins are for. There is no point in avoiding using them.
Update
In WordPress 3.6 support for native audio and video was added. Use the shortcodes https://wordpress.stackexchange.com/questions/71094/your/url and https://wordpress.stackexchange.com/questions/71094/your/url to embed these files and get proper players.