Andrew_W,
Download this
http://www.nchsoftware.com/prism/index.html - "Get it Free" the free version - and you will be able to play (and convert if required) your AVCHD .MTS files. After the installation go to "Options" > "Conversions" > "Decoder Options" and check "Use FFMPEG first...", then when you open an .MTS file Prism may automatically download on demand the ffmpeg component.
AVCHD is generally H.264 encoded video and AC-3 encoded audio which can make it difficult to decode if the correct codecs are not installed on a machine.
Best of luck,
4M2.
Edit: if your .MTS files are interlaced then I would not recommend Prism for conversion - only for playback. If you do wish to convert interlaced to another format, either retaining interlacing or with de-interlacing, then another program would be more suitable. Of the free programs "Handbrake" might be useful (?) but I haven't used it for a long time and the latest version may include those functions.
Edited by 4M2 (Tue 23-Aug-11 14:45:23)