Generalizable active mapping in complex unknown environments remains a critical challenge for mobile robots. Existing methods, constrained by limited training data and conservative exploration strategies, struggle to generalize across scenes with diverse layouts and complex connectivity. To enable scalable training and reliable evaluation, we present GLEAM-Bench, the first large-scale benchmark with 1,152 diverse 3D scenes from synthetic and real datasets. In this work, we propose GLEAM, a generalizable exploration policy for active mapping. Its superior generalizability comes from our semantic representations, long-term goal, and randomized strategies. It significantly outperforms state-of-the-art methods, achieving 68.16\% coverage (+11.41\%) with efficient trajectories, and improved mapping accuracy on 128 unseen complex scenes.