In many cultures throughout the world, it is customary for adult children to live with their parents. In fact, many generations live together in one house. This type of lifestyle encourages close family connections and the idea of relying upon each other for support. The taboo of living with one's parents in the United States is based on outdated ideals that children are supposed to do better than their parents, which is a near impossibility in the current economy.
Yes, if both the parents, and the adult children are happy with the arrangement, then there is no reason why they should not choose to live together. There can be a great benefit to both groups from the arrangement. Many elderly people suffer from loneliness and become less able to cope as they age, and many adult children cannot afford to live on their own if in low paying jobs.
I believe there are a lot of circumstances where it makes sense for adult children to live with their parents. While this hasn't been the precedent within the Western world, it's actually very common in other areas of the world. With so many low-wage jobs in America it is unlikely that a person can afford their own housing, grouping together is often easy for families and it can be valid reason to see adult children and their parents living together. Another circumstance that is a benefit to both is adult children helping their parent continue to live on their own.
Adult children should live with their parents; however, they should not be taking advantage of their parents. They should pay rent, food, utilities and other expenses just as they would if they were living with a roommate. They should also provide assistance to their parents, such as cooking meals, cleaning and driving to appointments.
Adult children should not live with their parents. They need the lessons that living on their own bring, such as learning to depend on yourself, taking care of your own bills, handling small situations that arise, shopping for yourself, etc. When adult children live with their parents, there is always that safety net of having someone who can pick up the slack for you. It hampers the confidence and independence that living on your own gives you.