Within the past half century, Integrated Circuits (ICs) experienced an aggressive, performance driven, technology feature size scaling. As the technology scaled into the deep nanometer range, physical and quantum mechanical effects that were previously irrelevant become influential, or even dominant, resulting in, e.g., not any longer negligible leakage currents. When attempting to pattern such small-geometry dimensions, the variability of technological parameters considerably gained importance. Furthermore, it became more difficult to reliably handle and integrate such a huge number of tiny transistors into large scale ICs, considering also that a substantial increase in power density needed to be taken into account. Scaling induced performance was no longer sufficient for delivering the expected improvements, which lead to a paradigm switch from uniprocessors to multiprocessor micro-architectures. At the same time, since for certain application domains, such as big data and Internet of things, the to be processed data amount increases substantially, computing system designers become more concerned with ensuring data availability than with reducing functional units latency. As a result, state of the art computing systems employ complex memory hierarchies, consisting of up to four cache levels with multiple shared scenarios, making memory a dominant design element that considerably influences the overall system performance and correct behavior. In this context, 3D Stacked Integrated Circuit (3D SIC) technology emerges as a promising avenue in enabling new design opportunities since it provides the means to interconnect devices with short vertical wires. In this thesis we address the above mentioned memory challenges by investigating the 3D SIC technology utilization in memory designs, as follows. First, we propose a novel banked multi-port polyhedral memory that provides an enriched access mechanism set with a very low bank conflict rate and we evaluate its potential in shared caches. Second, we propose a low power hybrid memory in which 3D technology allows for the smooth co-integration of: (i) short circuit current free Nano-Electro-Mechanical Field Effect Transistor (NEMFET) based inverters for data storage, and, (ii) CMOS-based logic for read/write operations and data preservation. Third, we propose a memory repair framework that exploits the 3D vertical proximity for inter-die redundant resources sharing. Finally, we propose novel schemes for performing user transparent multi-error correction and detection, with the same or even lower redundancy than the one required by state of the art extended Hamming single error correction schemes.