Online marketplaces are the main engines of legal and illegal e-commerce, yet their empirical properties are poorly understood due to the absence of large-scale data. We analyze two comprehensive datasets containing 245M transactions (16B USD) that took place on online marketplaces between 2010 and 2021, covering 28 dark web marketplaces, i.e., unregulated markets whose main currency is Bitcoin, and 144 product markets of one popular regulated e-commerce platform. We show that transactions in online marketplaces exhibit strikingly similar patterns despite significant differences in language, lifetimes, products, regulation, and technology. Specifically, we find remarkable regularities in the distributions of transaction amounts, number of transactions, inter-event times and time between first and last transactions. We show that buyer behavior is affected by the memory of past interactions and use this insight to propose a model of network formation reproducing our main empirical observations. Our findings have implications for understanding market power on online marketplaces as well as inter-marketplace competition, and provide empirical foundation for theoretical economic models of online marketplaces.