Many real-world data comes in the form of graphs, such as social networks and protein structure. To fully utilize the information contained in graph data, a new family of machine learning (ML) models, namely graph neural networks (GNNs), has been introduced. Previous studies have shown that machine learning models are vulnerable to privacy attacks. However, most of the current efforts concentrate on ML models trained on data from the Euclidean space, like images and texts. On the other hand, privacy risks stemming from GNNs remain largely unstudied. In this paper, we fill the gap by performing the first comprehensive analysis of node-level membership inference attacks against GNNs. We systematically define the threat models and propose three node-level membership inference attacks based on an adversary's background knowledge. Our evaluation on three GNN structures and four benchmark datasets shows that GNNs are vulnerable to node-level membership inference even when the adversary has minimal background knowledge. Besides, we show that graph density and feature similarity have a major impact on the attack's success. We further investigate two defense mechanisms and the empirical results indicate that these defenses can reduce the attack performance but with moderate utility loss.