It is not necessary for a multi engine propeller aircraft to have engines rotating in opposite direction (counter rotating propellers). As a matter of fact, most of the heavy turboprop aircraft such as the Dash 8, ATR, Fokker 50, Saab 340 etc have engines rotating in the same direction. That is they have co-rotating propellers. Yes, it is possible to have engines rotating the same direction, but have gearboxes to make the propellers turn the other direction. But this system is too complex and expensive.
The main issue with co-rotating propeller aircraft is the issue with the propeller P-factor. The P-factor is caused by the downgoing propeller blades experiencing a higher angle of attack than the up going blades. This causes the thrust vector of the propeller to offset. The result is shown in the picture below. The picture depicts a C-130. It has four turboprope engines and when looking from behind all of the engines rotate clockwise. The black arrows on each of the engines represent the thrust vector on them, while the red arrows represent the net thrust on each side of the aircraft. The black arrows are all shifted to the right because that is the side of the down going blades and it causes the thrust vector to offset.
The result of P-factor is that it requires a rudder input every time you add power. Again, looking at the C-130, you can see the net thrust is more to the right on the right side of the aircraft (looking from behind). So, as you add power, to keep the aircraft on the runway center line or on the right flight trajectory right rudder input will be required. The other issue comes when you have an engine failure. Airplanes with co-rotating propellers have what we call a critical engine. By definition, a critical engine is an engine whose failure will result in the highest unwanted yaw. In case of the C-130, the left outboard engine is the critical engine because if it fails, the highly shifted net thrust on the right side of the aircraft will cause the aircraft to yaw towards left. In two engine co-rotating turboprops it is the same story. The left engine is usually the critical engine. As pilots, it is hardly an issue. I flew Dash 8s for sometime in the start of my airline career. And failing the critical engine is always a part of our check rides carried out every six months. With the critical engine failure, the amount of rudder required increases but it is a non-event for a trained pilot. If you look at transport category turboprops you will notice how big the vertical stabilizer is compared to the size of the aircraft. The reason for this is to account for critical engine failures particularly on take offs.
Take note of the very bulky vertical stabilizer of this Dash 8 Q200. (Source: https://www.airliners.net/photo/USA-Army-Dynamic-Avlease/Bombardier-DHC-8-202Q-Dash-8/2081367)
There are many GA multi engine aircraft with counter rotating aircraft. The aircraft I did my multi engine training, the Piper Seneca II had such engines. It had no effects of torque or P-factor as the thrust lines in both the engines are shifted inwards. It had the handling of a jet aircraft. You could fly it without no real input on the rudder. I believe it is a marketing thing in the GA world. One could say it is far more safer in an engine out condition.
In jet powered aircraft, such tendencies do not exist. There is no torque or P-factor. It keeps a straight line if you add or remove thrust. So, it does not really matter how the engines rotate in jet aircraft.