By far the most common is supervised learning (in which there is a target variable). Less common is unsupervised learning (in which there is no target variable, but solution quality still might be measurable). Occasionally, one comes across reinforcement learning (long-term performance is measurable, but little or no short-term feedback is available), and a variety of more special-purpose techniques like association rule discovery / link analysis, anomaly detection, sequential patterns mining, frequent pattern mining and probably several others I've forgotten.