In this paper, we propose a new approach for recognizing intentions of humans by observing their activities with a color plus depth (RGB-D) camera. Activities and goals are modeled as a distributed network of inter-connected nodes in an Activation Spreading Network (ASN). Inspired by a formalism in hierarchical task networks, the structure of the network captures the hierarchical relationship between high-level goals and low-level activities that realize these goals. Our approach can detect intentions before they are realized and it can work in real-time. We also extend the formalism of ASNs to incorporate contextual information into intent recognition. We further augment the ASN formalism with special nodes and synaptic connections to model ordering constraints between actions, in order to represent and handle partial-order plans in our ASN. A fully functioning system is developed for experimental evaluation. We implemented a robotic system that uses our intent recognition to naturally interact with the user. Our ASN based intent recognizer is tested against three different scenarios involving everyday activities performed by a subject, and our results show that the proposed approach is able to detect low-level activities and recognize high-level intentions effectively in real-time. Further analysis shows that contextual and partial-order ASNs are able to discriminate between otherwise ambiguous goals.