When I see someone rev the engine on their car, it is typical for one side to drop a little in relation to the other. I understand that this is due to the torque of the engine. Why isn't the engine positioned so that the torque pushes down on the wheels that are providing the pull, as that would seem to result in better traction?
If you think about it, the torque actually does help. The reason for this is since the engine (in most cases) spins clockwise (looking from the grill backwards), the affected torque is transmitted CCW making the vehicle "roll" opposite of the engine spin. The driveshaft will (in the forward gears) also spin CW. As it spins, the torque will naturally lift the right side of the axle (as realized from the driver's seat) yet the torque will be pushing the body of the vehicle down on the same side. This behavior counteracts the torque and helps plant the rear wheel which is being lifted.
It doesn't mean much in a front wheel drive car, as the engine is transverse instead of longitudinal with most RWD vehicles. There's not much body torque which will occur there.
Huh? That's your question, really? The engine has a spinning crankshaft. You can design the system to spin clockwise or counterclockwise. Pick one.
You can mount an engine with its crankshaft oriented in alignment with vehicle centerline or transverse. Pick one.
Note that the majority of screw fasteners are designed to tighten when turned clockwise (and that tooling is very expensive). Re-evaluate the two decisions you made above analyzing the fasteners in your system.
Now you tell me what happens when you apply engine power to your system. It's very predictable.
Note there are some interesting design alternatives here. An example is a dual engine, dual propellor shaft boat. One engine spins clockwise (CW) the other spins counter clockwise (CCW). You have to be careful with the CCW engine as some of the fasteners used need to be left hand threads.
It is as Paulster wrote, the torque usually is canceled out, though I'm not sure if he got it correctly.
When a motor spins clockwise, it applies clockwise torque to the shaft and, as Newton said, encounters a counter-clockwise torque which it applies to the frame. The interesting point is, that the shaft applies the exactly same clockwise torque to the body of the next gearbox, which in turn puts this torque on the frame, canceling out the torque of the motor body. Yet, this might twist the frame a little, but since there is no net torque, this will not cause the car to roll.
Of course, the gearbox will apply a second torque to the frame contrary to the rotation direction of the output shaft, but then, there is the differential, which again behaves like the gearbox. Finally, the torque is applied to the street by the wheels, and since the car is not tied to the street, this is the point where torque is converted into movement of the frame.
Now, this is not absolutely correct. If the car accelerates, the rotating speed of all the rotating parts accelerates, too, and this of course "consumes" some torque. This definitely puts toque on the frame which is not canceled out, and could let the car roll. But most of the torque is lead to the wheels, and only a small fraction is needed to accelerate the rotating parts. This is a little different when the clutch is not engaged and the motor can rev up quite fast, and then, you can notice that the car might to a roll movement.
Further more: Most rear and 4wd driven cars have the motors built in laterally, while most front driven cars have the motor built in transversally. Otherwise, another gear to change the direction of the output shaft by 90° would be needed, which means additional losses.
On front driven cars, the motor sits about over the front axles, which means any torque applied to the frame by the motor would not cause an increase or decrease of "weight" on the front wheels, only on the rear wheels. And then, well, lets assume a torque of 200Nm and 2m distance to the rear wheels, this gives a "weight" of 10kg, which is about nothing (and doesn't matter, since that wheels are not driven)
A little off-topic:
Torque applied to the frame is a topic for propeller-driven aircraft, since they put the air into a swirling motion, i.e. apply torque to the air. Plus, the motors can make up a large fraction of the entire aircraft weight. On many two-engine aircraft, the one motor spins clockwise, while the other spins counter-clockwise. For example, see this PA-42, where the mirrored propellers indicate a different direction of rotation for both motors.