Complex systems produce recognizable self-organized patterns across time. This conceptual paper consists of a systematic reflection on what kinds of archetypical patterns systems can show, and in what kinds of cases these patterns could occur. Agent-based models are used to exemplify each pattern. We present a classification of the breadth of typical patterns that agent-based models can show when one runs them. The patterns fall into three categories: resource use, contagion, and output patterns. These are pattern archetypes; most real-world systems, and also most models, could and will show combinations of the patterns. In real systems, the patterns will occur as phases and building blocks of developments. These are patterns frequently occurring in real-world systems. The classification is the first of its kind. It provides a way of thinking and a language to non-mathematicians. This classification should be beneficial to those researchers who are familiar with a real-world pattern in their discipline of interest, and try to get a grasp of pattern causation. It can also serve in education, for giving students from a variety of disciplines an idea of the possibilities of agent-based models.