Training Deep Neural Networks (DNNs) is resource-intensive and time-consuming. While prior research has explored many different ways of reducing DNN training time, the impact of input data pipeline, i.e., fetching raw data items from storage and performing data pre-processing in memory, has been relatively unexplored. This paper makes the following contributions: (1) We present the first comprehensive analysis of how the input data pipeline affects the training time of widely-used computer vision and audio Deep Neural Networks (DNNs), that typically involve complex data preprocessing. We analyze nine different models across three tasks and four datasets while varying factors such as the amount of memory, number of CPU threads, storage device, GPU generation etc on servers that are a part of a large production cluster at Microsoft. We find that in many cases, DNN training time is dominated by data stall time: time spent waiting for data to be fetched and preprocessed. (2) We build a tool, DS-Analyzer to precisely measure data stalls using a differential technique, and perform predictive what-if analysis on data stalls. (3) Finally, based on the insights from our analysis, we design and implement three simple but effective techniques in a data-loading library, CoorDL, to mitigate data stalls. Our experiments on a range of DNN tasks, models, datasets, and hardware configs show that when PyTorch uses CoorDL instead of the state-of-the-art DALI data loading library, DNN training time is reduced significantly (by as much as 5x on a single server).