The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these data. We consider graph generation across multiple subfields, such as Semantic Web, graph databases, social networks, and community detection, along with general graphs. Despite the disparate requirements of modern graph generators throughout these communities, we analyze them under a common umbrella, reaching out the functionalities, the practical usage, and their supported operations. We argue that this classification is serving the need of providing scientists, researchers and practitioners with the right data generator at hand for their work. This survey provides a comprehensive overview of the state-of-the-art graph generators by focusing on those that are pertinent and suitable for several data-intensive tasks. Finally, we discuss open challenges and missing requirements of current graph generators along with their future extensions to new emerging fields.