From a purely physics point of view, you should always back into a parking spot. The reasons are simple, if you pull into a parking spot, since your back wheels don't turn, there's no way to straighten out the back of the car while the front of your car is half way in the parking spot. This is especially true in narrow parking spots. If you turn your steering wheel, the car will either go diagonally into the spot or the entire car will move closer to one side of the spot depending on which way you turn the wheel. Meanwhile, when you back into a spot, you can still straighten out the front of the car once you are halfway in the spot as you can just move the front of the car from side to side moving by turning the wheel.
The advantage of backing in is even more evident when pulling out. If you are pulling out of a tight parking spot, you can start to turn you wheel once your car is halfway out of the spot without hitting a car next to you. When you have to back out of a tight spot, you can't fully turn your wheel until the front of the car has cleared the cars next to you. This usually means that you are already fully into the aisle before you can turn your wheels to drive down the aisle. If there is not a lot of room between the row that you are in and the row across from you this can pose a problem as it usually takes a lot of going back and force to get your car in a position to drive away.