If you need to convert .mts files to .mov (so that e.g. iMovie can import them), I found ffmpeg to be the best tool for the task (I don't want to install and run "free format converters" that are usually Windows-only and come from untrusted sources). This post is inspired by iMovie and MTS blog post.
First I tried just changing the container:
for x in *.MTS; do ffmpeg -i ${x} -c copy ${x/.MTS/.mov}; done
But QuickTime could not play sound from those files because of AC-3 codec. Also, the quality of the video playback was very poor. The other command I tried was:
for x in *.MTS; do ffmpeg -i ${x} -vcodec copy -acodec mp2 -ac 2 ${x/.MTS/.mov}; done
Now QuickTime was able to play the sound, but problems with video remained. iMovie was unable to import the resulting files anyway (silently: I got no error message, just nothing happened when trying to import).
The final command that is proven to work well is this:
for x in *.MTS; do ffmpeg -i ${x} -vcodec mpeg1video -acodec mp2 -ac 2 -sameq ${x/.MTS/.mov}; done
The video has been converted perfectly, and iMovie successfully imported the movies. Note the useful bash substitution of extension, ${x/.MTS/.mov}. Enjoy!