We use numerical simulations to examine the structure of merger remnants resulting from collisions of gas-rich spiral galaxies. When the gas fraction of the progenitors is small, the remnants structurally and kinematically resemble elliptical galaxies, in agreement with earlier work. However, if the progenitor disks are gas-dominated, new types of outcomes are possible, where a prominent disk may survive in certain cases. To illustrate this scenario, we analyze an extreme example with progenitor galaxies consisting of dark matter halos, pure gas disks, and no bulges, as might be appropriate for mergers at high redshifts. While rapid star formation triggered by tidal torques during the merger forms a central, rotating bulge in the remnant, not all the gas is consumed in the burst. The remaining gas cools quickly and settles into an extended star-forming disk, yielding an object similar to a spiral galaxy and not an early-type galaxy. This is contrary to the usual view that major mergers invariably destroy disks. The morphological evolution of galaxies can therefore be more complicated than often assumed, and in particular, theoretical constraints based on the fragility of spiral disks need to be reevaluated.