Silicon technology scaling is continuously enabling denser integration capabilities. However, this comes at the expense of higher variability and susceptibility to wear-out. With an escalating number of on-chip components expected to be defective in near-future chips, modern parallel systems, such as Chip Multi-Processors (CMP), become especially vulnerable to these faults. Just a single link failure in the underlying Network on-Chip (NoC) may cause inter-tile communication to halt and even deadlock, rendering the chip useless. While fault-tolerant routing schemes do exist, they can only handle a finite number of link faults. In this paper, we address permanent wire failures which can occur in on-chip parallel links at manufacture-time or while in operation. Instead of marking the entire link as faulty, we present a methodology where the Partially Faulty Link (PFL) can still be used to transfer data between NoC routers, thus maintaining network connectivity, extending the yield and lifetime of the chip, and allowing for graceful performance degradation. To achieve this, we devise architectural augmentations both to the router and link micro-architectures, along with link fault detection, diagnosis, and re-configuration at the level of wire granularity. Statistical link-level fault models present the usability of PFLs, while relevant load-balancing routing algorithms and low-cost re-transmission mechanisms are also presented and coupled to the proposed architecture. Hardware synthesis demonstrates the feasibility of the proposed extensions to the base NoC architecture. Results obtained from full-system simulations show that high-performance NoCs are realizable in the presence of PFLs.