How can I play MTS videos from my Sony camera on my Mac?

Though Quicktime does not (and I couldn't find a codec plugin to support it), VLC apparently plays AVCHD video files (.mts). There is also a way to use VLC to transcode any video it can play to another format.

I use ClipWrap to rewrap the .mts file. then it can play without any problem.

As of iPhoto 9.3, iPhoto now supports AVCHD. So the officially sanctioned way to add such support for iPhoto now seems to be to install version 9.3.

There's a QuickTime plugin from Panasonic:

AVCCAM Importer

QuickTime Plug-in component

The AVCCAM Importer QuickTime plug-in component is to enable direct editing of AVCHD ".mts" file (*1) without conversion. AVCHD clips recorded on a Panasonic AVCCAM lineup product can be handled directly in QuickTime Player and Final Cut Pro.