An important aspect of human perception is anticipation, which we use extensively in our day-to-day activities when interacting with other humans as well as with our surroundings. Anticipating which activities will a human do next (and how) can enable an assistive robot to plan ahead for reactive responses. Furthermore, anticipation can even improve the detection accuracy of past activities. The challenge, however, is two-fold: We need to capture the rich context for modeling the activities and object affordances, and we need to anticipate the distribution over a large space of future human activities. In this work, we represent each possible future using an anticipatory temporal conditional random field (ATCRF) that models the rich spatial-temporal relations through object affordances. We then consider each ATCRF as a particle and represent the distribution over the potential futures using a set of particles. In extensive evaluation on CAD-120 human activity RGB-D dataset, we first show that anticipation improves the state-of-the-art detection results. We then show that for new subjects (not seen in the training set), we obtain an activity anticipation accuracy (defined as whether one of top three predictions actually happened) of 84.1, 74.4 and 62.2 percent for an anticipation time of 1, 3 and 10 seconds respectively. Finally, we also show a robot using our algorithm for performing a few reactive responses.