We suggest that at least some globular clusters are formed during the interaction or merger of galaxies. Such events could explain the disk population of clusters in the Galaxy, the young globulars in the Magellanic Clouds, the excess of clusters around ellipticals relative to spirals of the same luminosity and the anomalously large globular cluster systems around some galaxies in the center of galaxy clusters. We show that if all protospirals contain subgalactic clouds with a similar mass spectrum, the specific frequency of globular clusters around spirals will be constant. Extending the argument allows us to predict, for a given cosmological spectrum of density fluctuations, the number of globular clusters that form as a function of galactic mass. It also allows us to estimate the number of clusters formed in galaxy interactions and mergers. We show that our hypothesis is consistent with a number of current observations and describe possible tests of the model. These tests include direct observations of newly formed globular clusters in ongoing mergers and predictions about the number and metallicity of clusters as a function of radius in elliptical galaxies.