Objective: The growing availability of rich clinical data such as patients' electronic health records provide great opportunities to address a broad range of real-world questions in medicine. At the same time, artificial intelligence and machine learning (ML)-based approaches have shown great premise on extracting insights from those data and helping with various clinical problems. The goal of this study is to conduct a systematic comparative study of different ML algorithms for several predictive modeling problems in urgent care. Design: We assess the performance of 4 benchmark prediction tasks (eg mortality and prediction, differential diagnostics, and disease marker discovery) using medical histories, physiological time-series, and demographics data from the Medical Information Mart for Intensive Care (MIMIC-III) database. Measurements: For each given task, performance was estimated using standard measures including the area under the receiver operating characteristic (AUC) curve, F-1 score, sensitivity, and specificity. Microaveraged AUC was used for multiclass classification models. Results and Discussion: Our results suggest that recurrent neural networks show the most promise in mortality prediction where temporal patterns in physiologic features alone can capture in-hospital mortality risk (AUC>0.90). Temporal models did not provide additional benefit compared to deep models in differential diagnostics. When comparing the training-testing behaviors of readmission and mortality models, we illustrate that readmission risk may be independent of patient stability at discharge. We also introduce a multiclass prediction scheme for length of stay which preserves sensitivity and AUC with outliers of increasing duration despite decrease in sample size.