Many of the new quests, mainly in the Pandaren starting area have their respective cinematic videos to go with them, similar to Wrathgate. Note that many of the videos contain spoilers from the Pandaren starting area and such, so view then at your own risk.
HORDE PANDARIA PROLOGUE
ALLIANCE PANDARIA PROLOGUE
SHEN-ZIN SU'S THORN // Pandaren starting area: you find out the whole land is just a giant turtle whose thorn needs to be cured in order to save the lives of all the Pandaren living on it.
BATTLE AT SERPENT'S HEART
Last but not least, WANDERING ISLE DEPARTURE - after you're done with all your quests in the Pandaren starting area and you choose your faction, this video is played. This video has been added only recently to the beta files.