Approximate computing is an emerging paradigm for error resilient applications as it leverages accuracy loss for improving power, energy, area, and/or performance of an application. The spectrum of error resilient applications includes the domains of Image and video processing, Artificial Intelligence (AI) and Machine Learning (ML), data analytics, and other Recognition, Mining, and Synthesis (RMS) applications. In this work, we address one of the most challenging question, i.e., how to systematically employ approximate computing in Convolution Neural Networks (CNNs), which are one of the most compute-intensive and the pivotal part of AI. Towards this, we propose a methodology to systematically analyze error resilience of deep CNNs and identify parameters that can be exploited for improving performance/efficiency of these networks for inference purposes. We also present a case study for significance-driven classification of filters for different convolutional layers, and propose to prune those having the least significance, and thereby enabling accuracy vs. efficiency tradeoffs by exploiting their resilience characteristics in a systematic way.