The Society for Worldwide Interbank Financial Telecommunication (SWIFT) provides a network for financial institutions to send and receive information about financial transactions in the form of secure standardized messages. Here we analyze the global network created by flows of a particular type of SWIFT message, MT103, between 2003 and 2013. MT103 (single customer credit transfer) is the most commonly sent SWIFT message type and therefore may be a useful measure of global economic activity. We find that certain aspects of the MT103 networks are notably affected by global political and economic events. For example, we see a large reduction in links beginning in 2007 possibly due to increased financial regulation, and we see a lasting effect of the financial crisis of 2007-9 demonstrated by a reduction in the number of messages sent. At the same time, however, the underlying structure of the MT103 networks remains quite stable during the period of study. The networks are well described by a tiered model also seen in many payment system networks, with a stable core of densely connected countries. In addition, the networks exhibit a strong community structure, the largest communities roughly corresponding to Europe, the former Soviet Union and the United States plus much of Latin American and Asia. The United States is consistently the most important country in the networks according to various metrics. The empirical analysis conducted here not only increases our understanding of the SWIFT MT103 network in particular, but also may lead to improved modeling of financial systems in general.