Whether adding songs to a playlist or groceries during an online shop, how do we decide what to choose next? We develop a model that predicts such open-ended, sequential choices using a process of cued retrieval from long-term memory. Using the past choice to cue subsequent retrievals, this model predicts the sequential purchases and response times of nearly 5 million grocery purchases made by more than 100,000 online shoppers. Products can be associated in different ways, such as by their episodic association or semantic overlap, and we find that consumers query multiple forms of associative knowledge when retrieving options. Attending to certain knowledge sources, as estimated by our model, predicts important retrieval errors, such as the propensity to forget or add unwanted products. Our results demonstrate how basic memory retrieval mechanisms shape choices in real-world, goal-directed tasks.