The Ogre library does not provide any video decoding internally. However, there are a few plugins written for Ogre that allow you to decode various codecs into an Ogre texture. In fact, there are three plugins: Theora, Directshow and FFmpeg.
This is the most stable/flexible plugin. Code repository last updated in 2010. Theora Video Plugin
This plugin has been developed using Directshow libraries, that's why is only available for Windows platforms. This plugin allows to use a video file as texture for a material, being able to play near any file that can be played in Windows Media Player.
You can find the DirectShow plugin in ogreaddons/videoplugin. More information here: DirectShowVMR9 Plugin.
Be aware, FFmpeg contains many codecs (mpeg1 & 2, mp3, divx, etc), some of which are patented and may be risky to use with out first paying royalty use rights.
A maintained FFmpeg video player for Ogre can be found at: https://github.com/scrawl/ogre-ffmpeg-videoplayer. It has been tested on Win32, Mac and Linux, but probably works on other platforms too.