We present a spatio-temporal energy minimization formulation for simultaneous video object discovery and co-segmentation across multiple videos containing irrelevant frames. Our approach overcomes a limitation that most existing video co-segmentation methods possess, i.e., they perform poorly when dealing with practical videos in which the target objects are not present in many frames. Our formulation incorporates a spatio-temporal auto-context model, which is combined with appearance modeling for superpixel labeling. The superpixel-level labels are propagated to the frame level through a multiple instance boosting algorithm with spatial reasoning, based on which frames containing the target object are identified. Our method only needs to be bootstrapped with the frame-level labels for a few video frames (e.g., usually 1 to 3) to indicate if they contain the target objects or not. Extensive experiments on four datasets validate the efficacy of our proposed method: 1) object segmentation from a single video on the SegTrack dataset, 2) object co-segmentation from multiple videos on a video co-segmentation dataset, and 3) joint object discovery and co-segmentation from multiple videos containing irrelevant frames on the MOViCS dataset and XJTU-Stevens, a new dataset that we introduce in this paper. The proposed method compares favorably with the state-of-the-art in all of these experiments.