What program [preferably free] will burn a mkv video file?

Nero 9 should not have any problems with burning a .mkv video. What errors do you get when trying to burn it?

If you mean you have burnt it to a disk but the disk won't play the video then this is probably nothing to do with Nero but a problem with device you are trying to play it on not being compatible or having the right codec support.

If you are trying to play the file on your TV have you checked the TV supports .mkv playback? Although many TV's have a USB port these days that does not mean you can necessarily just stick any video file on a flash drive, plug it in and it will play.

Without any details about the hardware [TV make and model] you are trying to play the file on it is difficult to give more focused help. It is very unlikely that Nero is the problem though. Check the manual to see what media extensions your TV can play.

If you have successfully played media files on your TV just by connecting a flash drive, have you thought about using a video converter to convert to another popular format like mp4. You can download and use the Freemake converter from here [it supports all popular formats for input and output]: http://www.freemake.com/free_video_converter/

Since Nero doesn't recognize mkv files, convert them to avi. If you need a converter there are plenty of free ones, I personally use Format Factory. It's not necessary to change programs, Nero is about the best there is.

The burning software I like the most is Ashampoo Burning. It's 100% free and can be downloaded here: http://bitly.com/1lAVobS

A burning software is a tool that you need to create new CDs and DVDs. To make them working properly you need to burn them with a good software. Ashampoo is a very modern and reliable software that I recommend. It has plenty of other functions (e.g. you can edit videos and create DVD menus)

Have a Look at the following and I believe it will help you. good luck

http://www.wondershare.com/dvd-burner/convert-mkv-...

http://www.mkv-to-dvd.com/