Memories that exploit three-dimensional (3D)-stacking technology, which integrate memory and logic dies in a single stack, are becoming popular. These memories, such as Hybrid Memory Cube (HMC), utilize a network-on-chip (NoC) design for connecting their internal structural organizations. This novel usage of NoC, in addition to aiding processing-in-memory capabilities, enables numerous benefits such as high bandwidth and memory-level parallelism. However, the implications of NoCs on the characteristics of 3D-stacked memories in terms of memory access latency and bandwidth have not been fully explored. This paper addresses this knowledge gap by (i) characterizing an HMC prototype on the AC-510 accelerator board and revealing its access latency behaviors, and (ii) by investigating the implications of such behaviors on system and software designs.