A couple in the DHC-8:
Once, had the F/D fail along with both autopilot and yaw damper channels during light chop. Tried to troubleshoot / reengage; got the F/D back after a couple of attempts, but the AP / YD wouldn't have it. Continued the flight (perfect VFR day); after landing maintenance took a look and wound up deferring the A/P and Y/D under the MEL. We finished up 4 more (short) legs in that configuration. It turned out to be a failure in the yaw damper servo, apparently overworking itself to death in the bumps.
Another during takeoff, right after V1 while initiating rotation (just before sunset, good VFR) the F/D went out along with a "AHRS DATA INVALID" message on the ADU. Continued the takeoff through clean-up to enroute climb until comfortably above nearby obtructions. On the climbout my ADI was now showing a 75 degree bank and 15 degree pitch down; returned for a visual approach and landing, as not only was our destination reporting heavy rain, but it would be night by the time we got there. Not a turbulence failure per se, but apparently an AHRS failure during accelleration and rotation; conceivably though, something similar could happen during moderate or greater turbulence.