  We analyze a suite of 33 cosmological simulations of the evolution of Milky
Way-mass galaxies in low-density environments. Our sample spans a broad range
of Hubble types at z=0, from nearly bulgeless disks to bulge-dominated
galaxies. Despite the fact that a large fraction of the bulge is typically in
place by z=1, we find no significant correlation between the morphology at z=1
and at z=0. The z=1 progenitors of disk galaxies span a range of morphologies,
including smooth disks, unstable disks, interacting galaxies and
bulge-dominated systems. By z=0.5, spiral arms and bars are largely in place
and the progenitor morphology is correlated with the final morphology. We next
focus on late-type galaxies with a bulge-to-total ratio B/T<0.3 at z=0. These
show a correlation between B/T at z=0 and the mass ratio of the largest merger
at z<2, as well as with the gas accretion rate at z>1. We find that the
galaxies with the lowest B/T tend to have a quiet baryon input history, with no
major mergers at z<2, and with a low and constant gas accretion rate that keeps
a stable angular-momentum direction. More violent merger or gas accretion
histories lead to galaxies with more prominent bulges. Most disk galaxies have
a bulge Sersic index n<2. The galaxies with the highest bulge Sersic index tend
to have histories of intense gas accretion and disk instability rather than
active mergers.
