This paper explores the integration of active machine learning (ML) for 6G networks, an area that remains under-explored yet holds potential. Unlike passive ML systems, active ML can be made to interact with the network environment. It actively selects informative and representative data points for training, thereby reducing the volume of data needed while accelerating the learning process. While active learning research mainly focuses on data annotation, we call for a network-centric active learning framework that considers both annotation (i.e., what is the label) and data acquisition (i.e., which and how many samples to collect). Moreover, we explore the synergy between generative artificial intelligence (AI) and active learning to overcome existing limitations in both active learning and generative AI. This paper also features a case study on a mmWave throughput prediction problem to demonstrate the practical benefits and improved performance of active learning for 6G networks. Furthermore, we discuss how the implications of active learning extend to numerous 6G network use cases. We highlight the potential of active learning based 6G networks to enhance computational efficiency, data annotation and acquisition efficiency, adaptability, and overall network intelligence. We conclude with a discussion on challenges and future research directions for active learning in 6G networks, including development of novel query strategies, distributed learning integration, and inclusion of human- and machine-in-the-loop learning.