An integrated circuit may include integrated memory that is formed from a chain of memory blocks. Each memory block may have configurable input and output circuits. The configurable input and output circuits may be interposed between memory circuitry such as a memory array from circuitry external to the memory circuitry. The configurable input and output circuits may have upstream and downstream memory block connection ports. In such a way, configurable input and output circuits in a first memory block may pass control and address signals and data to configurable input and output circuits in a second memory block. By using the configurable input and output circuits, the integrated memory in the integrated circuit may operate to accommodate large bandwidth flows without using the general routing fabric of the integrated circuit.