There are a number of advantages (and what some people consider disadvantages) with MKV files.
With DVDs or Blu-rays, you can rip only the main feature, and avoid storing all the extra content on your PC. (you can rip that too, if you wanted though)
Similarly, if there are multiple audio tracks for the film, you can rip only the most relevant one - for example the English DTS-HD track, and not the dubbed versions or the lower quality Dolby Digital tracks etc.
And if the film has a PCM audio track, you can convert that to multichannel FLAC, which is losslessly compressed, rather than being uncompressed.
This can add up to savings of anything from 5-25GB for each Blu-ray disc. (I find it's about 10GB on average)
Because you are only ripping the main feature to an MKV file, it also means that you don't have to deal with menus for DVDs and the film starts right away. (Blu-ray menus don't work in MC right now anyway)
Similarly, you can rip a TV show so that each individual episode is its own file, and you can access them directly without the menus.
One of the disadvantages with MKVs though, is that you actually have to do a little work when ripping them. You can rip to ISO with AnyDVD, or just rip the file structure off the disc with Media Center without having to make a decision. When ripping to MKV it will often give you a list of titles and audio tracks to choose from when creating the MKV file. There are things you can do to help automate this, but it's still a bit more work than simply ripping the disc as-is.