Do turbine engines on multi-engine aircraft rotate in opposite directions to offset torque?
Torque is less of a problem due to the effective roll damping of a wing, but gyro effects and prop wash are important. Gyro effects first became an issue with rotary engines in WW I. A rotary engine has its crankshaft fixed to the airplane, and both the cylinder block and the propeller rotate. This gives better cooling at low speed and produces a flywheel effect, so the engine runs more smoothly. But when you yaw, the gyro effect pitches the aircraft up or down, so any precise maneuvering becomes very hard.

With the increasing engine power in 1916 and 1917, this effect became so severe that geared engines were developed where the cylinders rotate in one direction and the propeller in the opposite direction. As a consequence, the propeller had only half the RPM in air as it had with the cylinder block. This gave great propeller efficiency, but also big propeller diameters, so airplanes with those engines needed a high landing gear. Below is a picture of a Roland D XVI with a Siemens &amp; Halske III counter-rotating rotary engine from 1918 (source). This was an excellent fighter aircraft for its time with almost no gyro coupling.



Today, high power propeller aircraft tend to use identical engines but left- and right-handed gearboxes so the propellers run in both directions. This is less due to gyro effects and mostly to produce benign stall characteristics. The prop wash of a propeller increases the local angle of attack on the wing on one side and decreases it on the other side, so the wing will stall first on the side with bigger angle of attack. If this side is always to the right of the propellers, the aircraft will roll right in a stall. In the WW II period, a number of multi-engined aircraft used left-hand and right-hand turning engines in order to have the prop wash cancel out.

With jets, the rotating inertias are much smaller because the diameters are smaller. But there is one exception: The Bristol-Siddeley Pegasus engine of the Kestrel, Harrier and AV-8B jump jets needs to have the low pressure spool run in opposite direction of the high pressure spool to balance its gyro effects. If that would not be the case, a yawing motion would produce a pitching motion, and vice versa. When you sit on a jet, the thrust of which is equivalent to your weight, tilting this jet fore or aft only slightly will produce a quick shift of your location, so any maneuvering in hover will become extremely hard. 



USMC AV-8B Harrier in hover (picture source)