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Odometry consists in using data from a moving sensor to estimate change in position over time. It is a crucial step for several applications in robotics and computer vision. This paper presents a novel approach for estimating the relative motion between successive RGB-D frames that uses plane-primitives instead of point features. The planes in the scene are extracted and the motion estimation is cast as a plane-to-plane registration problem with a closed-form solution. Point features are only extracted in the cases where the plane surface configuration is insufficient to determine motion with no ambiguity. The initial estimate is refined in a photo-geometric optimization step that takes full advantage of the plane detection and simultaneous availability of depth and visual appearance cues. Extensive experiments show that our plane-based approach is as accurate as state-of-the-art point-based approaches when the camera displacement is small, and significantly outperforms them in case of wide-baseline and/or dynamic foreground.