Graph Neural Networks (GNNs) have been shown to be powerful in a wide range of graph-related tasks. While there exist various GNN models, a critical common ingredient is neighborhood aggregation, where the embedding of each node is updated by referring to the embedding of its neighbors. This paper aims to provide a better understanding of this mechanism by asking the following question: Is neighborhood aggregation always necessary and beneficial? In short, the answer is no. We carve out two conditions under which neighborhood aggregation is not helpful: (1) when a node's neighbors are highly dissimilar and (2) when a node's embedding is already similar to that of its neighbors. We propose novel metrics that quantitatively measure these two circumstances and integrate them into an Adaptive-layer module. Our experiments show that allowing for node-specific aggregation degrees have significant advantage over current GNNs.