In this paper, a robust RGB-D SLAM system is proposed to utilize the structural information in indoor scenes, allowing for accurate tracking and efficient dense mapping on a CPU. Prior works have used the Manhattan World (MW) assumption to estimate low-drift camera pose, in turn limiting the applications of such systems. This paper, in contrast, proposes a novel approach delivering robust tracking in MW and non-MW environments. We check orthogonal relations between planes to directly detect Manhattan Frames, modeling the scene as a Mixture of Manhattan Frames. For MW scenes, we decouple pose estimation and provide a novel drift-free rotation estimation based on Manhattan Frame observations. For translation estimation in MW scenes and full camera pose estimation in non-MW scenes, we make use of point, line and plane features for robust tracking in challenging scenes. Additionally, by exploiting plane features detected in each frame, we also propose an efficient surfel-based dense mapping strategy, which divides each image into planar and non-planar regions. Planar surfels are initialized directly from sparse planes in our map while non-planar surfels are built by extracting superpixels. We evaluate our method on public benchmarks for pose estimation, drift and reconstruction accuracy, achieving superior performance compared to other state-of-the-art methods. We will open-source our code in the future.