Embodied AI and robotic systems increasingly depend on scalable, diverse, and physically grounded 3D content for simulation-based training and real-world deployment. While 3D generative modeling has advanced rapidly, embodied applications impose requirements far beyond visual realism: generated objects must carry kinematic structure and material properties, scenes must support interaction and task execution, and the resulting content must bridge the gap between simulation and reality. This survey presents the first survey of 3D generation for embodied AI and organizes the literature around three roles that 3D generation plays in embodied systems. In \emph{Data Generator}, 3D generation produces simulation-ready objects and assets, including articulated, physically grounded, and deformable content for downstream interaction; in \emph{Simulation Environments}, it constructs interactive and task-oriented worlds, spanning structure-aware, controllable, and agentic scene generation; and in \emph{Sim2Real Bridge}, it supports digital twin reconstruction, data augmentation, and synthetic demonstrations for downstream robot learning and real-world transfer. We also show that the field is shifting from visual realism toward interaction readiness, and we identify the main bottlenecks, including limited physical annotations, the gap between geometric quality and physical validity, fragmented evaluation, and the persistent sim-to-real divide, that must be addressed for 3D generation to become a dependable foundation for embodied intelligence. Our project page is at https://3dgen4robot.github.io.