MKV file extension is one of the new file extension for videos used nowadays, its a good format and more commonly used in anime than in movies in general. Its as said on ther main website (www.matroska.org) a container its not a codec format like MPEG, Xvid or DivX so the only software you need is one that knows that.
Gom Player is one of the finest video player out there, its free, nice and fast. Want more reasons to download it? Try it! if you dont like it consider its free! :)
Go to this link to download the Software: http://www.gomlab.com/eng/GMP_download.html
Media Player Classic
Is one of the best video player, it main strength is its size and speed. It support most of the new codecs and splitters as MKV.
And if so far you are not decided... ITS FREE! :)
Go to this link to download the Software: http://sourceforge.net/projects/guliverkli/