So I capture it with RecordMyDesktop (I run xubuntu), and run through an ffmpeg script (https://github.com/choptastic/watchmecode) that resizes the video to be the same length as an MP3, and makes an X minute screencap montage for the client.
Then it produces something like this, which I did while working on a specific feature[2] for my sports league management system[1]: http://www.youtube.com/watch?v=Hwn7mfmo0SQ
In my experience, my clients basically find it interesting seeing a snippet of how a programmer works. I had one client who would show the video around in his office like it was the greatest thing since sliced bread. At first, I thought the reaction was sarcastic, but I realized after the 3rd time showing another employee, and his elderly father, that he was just genuinely impressed by it.
THAT SAID, if a client required this of me because they wanted to monitor me (to make sure I'm working or whatever), I'd let them know that "sure, I can do it for the most part, but I have to disable it when checking my email, and any time spend curating the video due to privacy concerns will be billed to you as well."
But if a client asked it of me to satisfy their own curiosity of my workflow (which is unlikely, since I typically just volunteer it anyway), I'd be more than happy to do it.
[1] http://bracketpal.com (homepage is still embarrassingly sparse, as I've been working one-on-one with customers, a landing page redesign and online customers are coming first).
[2] The video above is the screencap of the implementation of this feature: http://www.youtube.com/watch?v=zxTfaSfa_dQ