We have performed hydrodynamic simulations of galaxy formation in a LCDM universe. We have followed galaxy formation in a dark matter halo, chosen to have a relatively quiet recent merger history, using different models for star formation and feedback. In all cases, we have adopted a multi-phase description of the interstellar medium and modelled star formation in quiescent and burst modes. We have explored two triggers for starbursts: strong shocks and high gas density, allowing for the possibility that stars in the burst may form with a top-heavy initial mass function. We find that the final morphology of the galaxy is extremely sensitive to the modelling of star formation and feedback. Starting from identical initial conditions, galaxies spanning the wide range of Hubble types, with B-band disc-to-total luminosity ratios ranging from 0.25 to 0.9, can form in the same dark matter halo. Models in which starbursts are induced by high gas density (qualitatively similar to models in which feedback is produced by AGN) generate energetic winds and result in galaxies with an early-type morphology. Models in which the starbursts are induced by strong shocks lead to extended discs. In this case, the feedback associated with the bursts suppresses the collapse of baryons in small halos, helping to create a reservoir of hot gas that is available for cooling after $z = 1$, following the bulk of the dynamical activity that builds up the halo. This gas then cools to form a large, young stellar disc. Comment: 17 pages, 11 figures, accepted for Publication in MNRAS. Movies are available at http://star-www.dur.ac.uk/~takashi/research/movies.html