As robots venture into new application domains as autonomous vehicles on the road or as domestic helpers at home, they must recognize human intentions and behaviors in order to operate effectively. This paper investigates a new class of motion planning problems with uncertainty in human intention. We propose a method for constructing a practical model by assuming a finite set of unknown intentions. We first construct a motion model for each intention in the set and then combine these models together into a single Mixed Observability Markov Decision Process (MOMDP), which is a structured variant of the more common Partially Observable Markov Decision Process (POMDP). By leveraging the latest advances in POMDP/MOMDP approximation algorithms, we can construct and solve moderately complex models for interesting robotic tasks. Experiments in simulation and with an autonomous vehicle show that the proposed method outperforms common alternatives because of its ability in recognizing intentions and using the information effectively for decision making.