Does the yaw damper require manual activation on modern airliners?
787
On the 787 there is no activate/deactivate button for it. Yaw damping and turn coordination are always active as long as the flight controls law is in primary mode. In secondary or direct modes, yaw damping becomes degraded.
Primary being the fly-by-wire's fully functional mode. Source: 787 FCOM.

MD-11
On an older generation plane, for example the MD-11, there are buttons for the yaw damper, 4 in fact for the 4 channels, they are rarely used (always on) unless there's a fault and after troubleshooting you want to take a channel out.
(airliners.net) Four yaw damper buttons on the MD-11's overhead panel.

737 Next Generation
On a 737, after a flight is completed and the IRS knobs are moved to the off position, the yaw damper switch automatically goes to the off position.
I suspect the rationale back then (carried over from earlier 737 variants) was you can't have the switch on the &quot;on position&quot; and the fault light illuminated when there was no fault. (The yaw damper needs a functioning ADIRU, which needs input from the IRS.)

(airliners.net) Yaw damper and IRS controls on the 737 overhead panel.

Autopilot and yaw damper
In most (if not all) planes that come with a yaw damper (YD), engaging the autopilot (A/P) is not needed to enable the YD, i.e., you can hand fly and still have the YD on, whether there's a switch for it (737) or not (787).
In the MD-11 if all four channels failed, the A/P can only be used in cruise. So as you can see, you need the YD for the A/P in the MD-11, not the other way around. Source: MD-11 QRH.