Is trimming aircraft to relieve pilot of applying force on control stick/Pedal still applicable?
Almost all airplanes have trim (I'm fairly certain that the Wright Flyer didn't, so I can't say all airplanes do), but a lot of newer designs don't use trim tabs because they are less aerodynamically efficient than alternative designs.

For instance, the Falcon 50 &amp; 900 that I fly doesn't have a single trim tab on it.  Normally the flight controls are moved by hydraulics and a small electrical actuator is used to adjust the position of the aileron and rudder for trim purposes.  Pitch trim is accomplished by moving the front of the entire horizontal stabilizer in order to adjust the angle and amount of lift produced by the tail.  This is done so that the elevator can be neutralized and not create the additional drag caused by being in the airflow.



On FBW airplanes, they may or may not have manual trim that is used (under normal circumstances) by the pilot.   Trimming is still taking place on FBW airplanes without manual trim, but it is simply automated.

Boeing typically designs their FBW airplanes so that they behave like a "normal" airplane, and require the pilot to trim in order to relieve the control forces.  This is all completely artificial though, programmed simply to give feedback to the pilot.  

Airbus on the other hand doesn't give any feedback to the pilot through the side stick so there are no control forces to relieve.   When you release the side stick, it centers and the aircraft maintains its current pitch and bank angle.  In this case, the autopilot automatically trims the airplane for the current conditions, and the pilot doesn't need to worry about it.