A single engine plane can suffer from control problems due to torque.
An early famous example was the Sopwith Camel
As others have pointed out, torque effects have to be countered using the normal aerodynamic controls available to the pilot.
Some aircraft had extra-large ailerons because of this issue.
aviation.stackexchange.com/users/1289/RedGrittyBrick
In contrast to what happens in helicopters, the static and dynamic stability will prevent big movements of propeller aircraft due to engine and propeller torque.
The biggest consequence, the rolling moment, is taken care of by roll damping.
When the propeller torque rolls the aircraft, the downwards-moving wing will see a higher, and the upwards-moving wing a lower angle of attack.
Both wings will create a rolling moment which will quickly stop the rolling motion.
All the pilot has to do is to restore the correct roll attitude using the ailerons.
The lift difference of the rolling aircraft also creates different drag on the left and right wings, so a small yawing moment will turn the aircraft slightly sideways when the rolling starts.
This has to be corrected by rudder input.
If we look at other secondary effects, the yawing motion will cause a slight pitch change by way of engine and propeller precession.
This also will be stopped quickly by pitch damping (the pitch movement changes the angle of attack on the horizontal tail surfaces), and the pilot needs to correct the pitch attitude again.
In consequence, changing RPM will induce slight movements around all three axes in a single-engined propeller airplane.
aviation.stackexchange.com/users/1961/Peter Kämpf
It is countered by the natural stability and the roll control provided by the ailerons.
If you have insufficient airspeed for roll control then you will be on the ground and your gear will prevent excessive rolling.
aviation.stackexchange.com/users/609/ratchet freak
There is a big difference between the amount of torque delivered to the main rotor of a helicopter and that delivered to the propeller of a comparably-sized fixed wing aircraft.
Also, without the tail rotor, a helicopter in a hover has nothing to "push against" in order to deliver the needed torque to the main rotor.
If not for the tail rotor, torque delivered to the main rotor would cause the rest of the vehicle to spin up in the opposite direction.
Hovering flight would be pretty much impossible without something to aerodynamically generate opposing torque (tail rotor, second counter-rotating rotor, etc.).
Torque delivered to the propeller of a fixed-wing aircraft is opposed either through the ground (when stationary, taxiing or on take-off roll), or by the wings (with minor roll trim or control input) when in flight.
As explained in the other answers, propeller torque does induce certain effects, but they are of much less significance than that of a helicopter main rotor, and are dealt with by trim and pilot awareness/handling.
aviation.stackexchange.com/users/3218/Anthony X
Torque is more noticeable in aircraft with tail wheels (tail draggers) which also have large engines (e.g. world war 2 vintage) for two reasons: If the throttle is advanced too quickly, you might not have enough airflow over the rudder to be able to counteract it and a swing followed by a ground loop could result.
At the point when the tail is lifted off the ground during the take off run, gyroscopic effects occur that could cause a swing (try holding a spinning top and then move it around -
it exerts forces in unexpected directions).
Also on aircraft with the largest engines, the torque could make one wing lower than the other during the take off run.
You also have the problem going around to be very careful with both throttle and rudder because these effects are more pronounced at lower airspeeds where airflow is less.
An aeroplane with a nosewheel is generally more stable on the ground (due to the CG being ahead of the main wheels rather than behind), so these effects are less noticeable.
aviation.stackexchange.com/users/9679/Philip Johnson
Helicopters need a tail rotor to balance the torque reaction that tends to rotate the main body sideways. Doesnt a single-engine plane suffer the same problem? I would imagine that (for example) the left wing would dip lower than the right due to the torque. How is it countered?
Do aeroplanes have to balance torque like helicopters?
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aviation.stackexchange.com/users/3136/Jesvin Jose
 In airplanes torque is countered by the natural stability and the roll control provided by the ailerons. Torque delivered to the propeller of a fixed-wing aircraft is opposed either through the ground (when stationary, taxiing or on take-off roll), or by the wings (with minor roll trim or control input) when in flight. However, a single engine plane can suffer from control problems due to torque.   Torque can cause control problems in single engine planes. However, the natural stability and roll control provided by the ailerons counter torque. Torque delivered to the propeller of a fixed-wing aircraft is countered by the ground or by the wings.
Torque can cause control problems in single engine planes. The natural stability and roll control provided by the ailerons counter torque. Torque delivered to the propeller of a fixed-wing aircraft is countered by the ground or by the wings.