Courts really don't want to take control of every minute aspect of your life, even when you divorce and have kids. Judges prefer that you come up with your own parenting plan, which might include what parent will drop off the children and who will pick them up for visitation. Sometimes, however, parents just can't agree, so the court will get involved, making a ruling based on your family's unique circumstances and the best interests of the children.
Common Sense Measures
If you and your spouse plan to live some distance apart, consider setting up a halfway point where you can meet and exchange the kids. This will cut down on either parent taking the brunt of gas and other transportation expenses as well. Otherwise, it may make sense for the parent who is relinquishing the child at the end of parenting time to drop him off at the other parent's home. This avoids putting the child in a position where he feels like one parent is taking him away from the other, and it also ensures that the relinquishing parent – and the child – are ready for the transition.
Issues of Domestic Violence
If you and your spouse have a history of domestic violence, the court will almost certainly order a detailed parenting plan, including pick-up and drop-off rules, to minimize contact between you. This might involve a neutral third party handling the exchanges, picking up the children from one household and taking them to the other. A judge may order a meeting point for the exchange, even if you don't live far apart. This might be the parking lot at a police station, or another highly-trafficked and safe location.