In this paper, we provide an in-depth study of Stochastic Backpropagation (SBP) when training deep neural networks for standard image classification and object detection tasks. During backward propagation, SBP calculates gradients by using only a subset of feature maps to save GPU memory and computational cost. We interpret SBP as an efficient way to implement stochastic gradient decent by performing backpropagation dropout, which leads to significant memory saving and training run-time reduction, with a minimal impact on the overall model accuracy. We offer best practices to apply SBP for training image recognition models, which can be adopted in learning a wide range of deep neural networks. Experiments on image classification and object detection show that SBP can save up to 40% of GPU memory with less than 1% accuracy degradation. Code is available at: https://github.com/amazon-research/stochastic-backpropagation