Many information structures generate correlated rather than mutually independent signals, the news media being a prime example. This paper shows experimentally that in such contexts many people neglect these correlations in the updating process and treat correlated information as independent. In consequence, people's beliefs are excessively sensitive to well-connected information sources, implying a pattern of "overshooting" beliefs. Additionally, in an experimental asset market, correlation neglect not only drives overoptimism and overpessimism at the individual level, but also affects aggregate outcomes in a systematic manner. In particular, the excessive confidence swings caused by correlated signals give rise to predictable price bubbles and crashes. These findings are reminiscent of popular narratives according to which aggregate booms and busts might be driven by the spread of "stories". Our results also lend direct support to recent models of boundedly rational social learning.