Do the captain's and first officer's rudder pedals always move together?
In the EMB-145 and -135 the rudder controls are mechanically linked in the tail in an assembly that converts torque from the rudder cables to linear rod input into the rudder hydraulic control units.  Up until this assembly the rudders are technically independent and the cables for each rudder are routed differently through the airframe so that a single point of damage does not render the rudder inop.  The autopilot servo is only located on the captains rudder cables.  Through the rear linkage both pilots rudder pedals will move together when either provides input.

Our other controls are a bit more interesting.  The roll input is also linked, but it is linked at the control column,  Each yoke independently controls its own aileron -- the CA yoke only flies the left aileron and the FO yoke the right aileron.  It is only through the control column linkage that each yoke can control the whole airplane.  It is done this way so that if there is a problem with a cable jamming, the control interlock can be disconnected and at least half control regained.