Advances in deep learning and generative modeling have driven interest in data-driven molecule discovery pipelines, whereby machine learning (ML) models are used to filter and design novel molecules without requiring prohibitively expensive first-principles simulations. Although the discovery of novel molecules that extend the boundaries of known chemistry requires accurate out-of-distribution (OOD) predictions, ML models often struggle to generalize OOD. Furthermore, there are currently no systematic benchmarks for molecular OOD prediction tasks. We present BOOM, $\boldsymbol{b}$enchmarks for $\boldsymbol{o}$ut-$\boldsymbol{o}$f-distribution $\boldsymbol{m}$olecular property predictions -- a benchmark study of property-based out-of-distribution models for common molecular property prediction models. We evaluate more than 140 combinations of models and property prediction tasks to benchmark deep learning models on their OOD performance. Overall, we do not find any existing models that achieve strong OOD generalization across all tasks: even the top performing model exhibited an average OOD error 3x larger than in-distribution. We find that deep learning models with high inductive bias can perform well on OOD tasks with simple, specific properties. Although chemical foundation models with transfer and in-context learning offer a promising solution for limited training data scenarios, we find that current foundation models do not show strong OOD extrapolation capabilities. We perform extensive ablation experiments to highlight how OOD performance is impacted by data generation, pre-training, hyperparameter optimization, model architecture, and molecular representation. We propose that developing ML models with strong OOD generalization is a new frontier challenge in chemical ML model development. This open-source benchmark will be made available on Github.