I've noticed that when I burn rubber on takeoff, the rear end fishtails slightly to the right. I'd guess this has to do with the differential, but I can't remember all the particulars about pumpkins.

Can someone please explain the why's for me?

 

torque, plain and simple. if you rev you'll see the body twist to the right compressing the right rear suspension. when the tires break loose it follows the compressed suspension.

 

Multiple reasons. On some cars the axle's are slightly different lengths to account for diff placement, which causes a slight difference in torque at the rear wheels. Also because of the way power is transferred through the diff with the pinion gear offset on one side of the ring gear and the ring gear offset to one side of the diff. Also like was mentioned that when you accelerate the torque from engine rotation causes the vehicle to twist to the right increasing traction at the right rear wheel which works with the suspension to effect a weight transfer that favors one side of the car. The end result is that the right rear tire gets a bit more traction and the car tries to turn left, or the rear end steps out to the right.

It's called torque steer, and is more noticeable on higher powered cars, and particularly on front wheel drive cars due to the hugely different lengths of the half shafts(axles with u joints that are used on FWD and IRS).

 

Thanks for the explanations. I was thinking of it in opposite terms: the car fishtails to the right because the right rear tire is losing traction. The steering explanation is the easiest to understand, though.