Bob Moore writes:

Turned ON and OFF...Yes, but hardly at the pilot's discretion.

I don't know what the procedures say for the 737-800. I understand
that it isn't always on (not for takeoffs and landings).

I have no 737 experience, but the 727 has 2 rudders and 2 yaw
dampers. If just one of them fails, the pilot must descend below
30,000' and slow to a specified maximum speed, just in case the
other one should fail also.

One big difference is that the 727 had the split rudder, whereas the
737 (and successors) does not.

Here's an interesting but somewhat sensationalized article on
uncommanded rudder movements in the 737 (potentially blamed on the yaw
damper):

http://seattletimes.nwsource.com/news/local/737/part01/

This was in 1996; I'm not sure how things have evolved in the
following decade. It's not ideally relevant to this discussion, but
it's an interesting article (and a very long one).

I'm not sure why an inoperative yaw damper would be a no-go item, but
perhaps the unusual characteristics of the 727 made it so (?).

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