As technology scales, Network-on-Chips (NoCs), currently being used for on-chip communication in manycore architectures, face several problems including high network latency, excessive power consumption, and low reliability. Simultaneously addressing these problems is proving to be difficult due to the explosion of the design space and the complexity of handling many trade-offs. In this paper, we propose IntelliNoC, an intelligent NoC design framework which introduces architectural innovations and uses reinforcement learning to manage the design complexity and simultaneously optimize performance, energy-efficiency, and reliability in a holistic manner. IntelliNoC integrates three NoC architectural techniques: (1) multifunction adaptive channels (MFACs) to improve energy-efficiency; (2) adaptive error detection/correction and re-transmission control to enhance reliability; and (3) a stress-relaxing bypass feature which dynamically powers off NoC components to prevent overheating and fatigue. To handle the complex dynamic interactions induced by these techniques, we train a dynamic control policy using Q-learning, with the goal of providing improved fault-tolerance and performance while reducing power consumption and area overhead. Simulation using PARSEC benchmarks shows that our proposed IntelliNoC design improves energy-efficiency by 67% and mean-time-to-failure (MTTF) by 77%, and decreases end-to-end packet latency by 32% and area requirements by 25% over baseline NoC architecture.