We develop a general equilibrium model of self-fulfilling bank runs in a setting without aggregate risk. The key novelty is the way in which the banking system's assets and liabilities are connected. Banks issue loans to entrepreneurs who sell goods to households, which in turn pay for the goods by redeeming bank deposits. The return on bank assets is thus contingent on households being able to withdraw their deposits. In a run, not all households that wish to consume manage to withdraw, since part of banks' cash reserves end up in the hands of households without consumption needs. This lowers revenues of entrepreneurs, which causes some of them to default on their loans and thereby rationalises the run in the first place. Interventions that restrict redemptions in a run - such as deposit freezes - can be self-defeating due to their negative effect on demand in goods markets. We show how runs may be prevented with combinations of deposit freezes and redemption penalties as well as with the provision of emergency liquidity by central banks.