Arkanite has released a Work In Progress(WIP) Media Center for the PS Vita, here is a quote from the source:

A WIP media center application for the Playstation Vita.
Traveling for work at the moment and was looking for a small vita application to work on.

So far i have added support for Vitas native mp4 video formats.
* MPEG-4 Simple Profile Level 6, Maximum 1280 720 pixels, AAC
* H.264/MPEG-4 AVC Baseline/Main/High Profile Level 4.0, Maximum 1920 1080p, AAC
both video and audio must be compatible or the video simply wont play.

Initial release restriction:
- local playback only, from 'ux0:/data/media center/videos/', so all videos must be placed in this directory.
I will remove this restriction next, to allow for file browsing in all safe locations.
- limited gamepad support. not ideal for VitaTV yet, but basic playback and video selection is still achievable via gamepad. [ Register or Signin to view external links. ]