Movie textures if you have Pro edition.

http://unity3d.com/support/documentation/Manual/Video%20Files.html

Otherwise you'll have to wing it. You can set up cutscenes using triggers to activate certain cameras and movements, but I'm no expert in that department.

The way we have tackled this problem seems to work well.

Construct your cutscene in a separate level. The level should be built in a special way, so that all the GameObjects in the level are parented under one main GameObject which has a name like "CutScene1". Make sure all the GameObjects are in a layer called "CutScene". When the level loads, it should automatically start playing the animations, moving its camera, etc. The camera should only render objects on the CutScene layer.

Then, in your game world level, set things up so you can call LoadLevelAdditive("CutScene1") when needed. When it has loaded, set the new cut scene camera to render over your game world, and toggle your AudioListener components if required. When the cutscene finishes, make sure you clean up by destroying the "CutScene1" root GameObject, and your game world level should be left untouched.

Well If you have Unity 2.6.1 you can not put a movie file in. If you have Unity pro you can if I were you I would put together a ton of pictures and animate them. Like what they do cartoons.

well sense randycooper says you cant add a video

you could do pictures or create the animation in unity or a similar program like cinema 4d then simply trigger the animation in the game

(although i cant figure out the exporting animation part)