Deep learning based recommendation systems form the backbone of most personalized cloud services. Though the computer architecture community has recently started to take notice of deep recommendation inference, the resulting solutions have taken wildly different approaches - ranging from near memory processing to at-scale optimizations. To better design future hardware systems for deep recommendation inference, we must first systematically examine and characterize the underlying systems-level impact of design decisions across the different levels of the execution stack. In this paper, we characterize eight industry-representative deep recommendation models at three different levels of the execution stack: algorithms and software, systems platforms, and hardware microarchitectures. Through this cross-stack characterization, we first show that system deployment choices (i.e., CPUs or GPUs, batch size granularity) can give us up to 15x speedup. To better understand the bottlenecks for further optimization, we look at both software operator usage breakdown and CPU frontend and backend microarchitectural inefficiencies. Finally, we model the correlation between key algorithmic model architecture features and hardware bottlenecks, revealing the absence of a single dominant algorithmic component behind each hardware bottleneck.