We present a novel computationally efficient approach to obstacle detection that is applicable to both structured (e.g. indoor, road) and unstructured (e.g. off-road, grassy terrain) environments. In contrast to previous works that attempt to explicitly identify obstacles, we explicitly detect scene regions that are traversable - safe for the robot to go to - from its current position. Traversability is defined on a 2D grid of cells. Given 3D points, we map them to individual cells and compute histograms of elevations of the points in each cell. This elevation information is then used in a graph based algorithm to label all traversable cells. In this manner, positive and negative obstacles, as well as unknown regions are implicitly detected and avoided. Our notion of traversability does not make any flat-world assumptions and does not need sensor pitch-roll compensation. It also accounts for overhanging structures like tree branches. We demonstrate that our approach can be used with both lidar and stereo sensors even though the two sensors differ in their resolution and accuracy. We present several results from our real-time implementation on realistic environments using both lidar and stereo.