The ability to perform fast context-switching and massive multi-threading is the forte of modern GPU architectures, which have emerged as an efficient alternative to traditional chip-multiprocessors for parallel workloads. One of the main benefits of such architecture is its latency-hiding capability. However, the efficacy of GPU's latency-hiding varies significantly across GPGPU applications. To investigate this, this paper first proposes a new algorithm that profiles execution behavior of GPGPU applications. We characterize latencies caused by various pipeline hazards, memory accesses, synchronization primitives, and the warp scheduler. Our results show that the current round-robin warp scheduler works well in overlapping various latency stalls with the execution of other available warps for only a few GPGPU applications. For other applications, there is an excessive latency stall that cannot be hidden by the scheduler effectively. With the latency characterization insight, we observe a significant execution time disparity for warps within the same thread block, which causes sub-optimal performance, called the warp criticality problem. To tackle the warp criticality problem, we design a family of criticality-aware warp scheduling (CAWS) policies by scheduling the critical warp(s) more frequently than other warps. Our results on the breadth-first-search, B+tree search, two point angular correlation function, and K-means clustering show that, with oracle knowledge of warp criticality, our best-performing scheduling policy can improve GPGPU applications' performance by 17% on average. With our designed criticality predictor, the various scheduling policies can improve performance by 10-21% on breadth-first-search. To our knowledge, this is the first paper to characterize warp criticality and explore different criticality-aware warp scheduling policies for GPGPU workloads.