Intelligent agents that are intended to work in dynamic environments must be able to gracefully handle unsuccessful tasks and plans. In addition, such agents should be able to make rational decisions about an appropriate course of action, which may include aborting a task or plan,either as a result of the agent's own deliberations, or potentially at the request of another agent. In this paper we investigate the incorporation of aborts into a BDI-style architecture. We discuss some conditions under which aborting a task or plan is appropriate, and how to determine the consequences of such a decision. We augment each plan with an optional abort-method, analogous to the failure method found in some agent programming languages. We provide an operational semantics for the execution cycle in the presence of aborts in the abstract agent language CAN, which enables us to specify a BDI-based execution model without limiting our attention to a particular agent system (such as JACK, Jadex, Jason, or SPARK). A key technical challenge we address is the presence of parallel execution threads and of sub-tasks, which require the agent to ensure that the abort methods for each plan are carried out in an appropriate sequence.