Continuous technology scaling has made aging mechanisms, such as negative bias temperature instability and electromigration primary concerns in network-on-chip (NoC) designs. In this paper, we extensively analyze the effects of these aging mechanisms on NoC routers and links. We observe a critical need of a robust aging-aware routing algorithm that not only reduces power-performance overheads caused due to aging degradation, but also minimizes the stress experienced by heavily utilized routers and links. To solve this problem, we propose an aging-aware adaptive routing algorithm and a router microarchitecture that routes the packets along the paths, which are both least congested and experience minimum aging degradation. After an extensive experimental analysis using real workloads, we observe 13% and 12.17% average overhead reduction in network latency and energy-delay product per flit, a 10.4% improvement in performance, and a 60% improvement in mean time to failure using our aging-aware routing algorithm.