MKV is technically not a 'video' format, as much as it's a container format (in otherwords, it holds different audio tracks, subtitle tracks, and video tracks etc. with in).
As such, MKV isn't really supported on anything except a computer, that I know of anyway, and even then it require special codecs (altough the new DivX supports MKV - I've yet to have anything play properly in it with out the CCCP codec pack).
The PlayBook supports MP4, h.264, WMV, DivX/Xvid AVI (depending on how it's encoded). For the most part, you will find issues with some formats not playing properly - this is typically because the settings are not optimized for proper playback on this type of device. Most H.264 formats, like mp4, WMV, etc. require a lot of CPU power to decode and some will choke (even on a desktop computer a lot of times a poorly encoded 1080p MP4 file can have issues).
I have numerous 720p mp4 files loaded on my Playbook and they play beautifully. I've also got a couple of WMV files and DivX files that also play without a hiccup. But these are all files I've encoded (I own a video production company, so they're samples of our work) - but not a hiccup anywhere. I did have issues playing back a 1080p WMV file though - but haven't played around to see why.
If you are downloading MKV files, you'll need to transcode them to mp4 or Divx, as someone else mentioned. I don't know what programs would be best for this off hand... but I know there's quite a few out there.