Disk galaxies are common in our universe and this is a source of concern for hierarchical formation models like ΛCDM. Here we investigate this issue as motivated by raw merger statistics derived for galaxy-size dark matter halos from ΛCDM simulations. Our analysis shows that a majority (~ 70%) of galaxy halos with M0 = 1012M⊙ at z = 0 should have accreted at least one object with mass m > 1011M⊙ ≃ 3 Mdisk over the last 10 Gyr. Mergers involving larger objects m ≳ 3 × 1011M⊙ should have been very rare for Milky-Way size halos today, and this pinpoints m/M ~ 0.1 mass-ratio mergers as the most worrying ones for the survival of thin galactic disks. Motivated by these results, we use use high-resolution, dissipationless N-body simulations to study the response of stellar Milky-Way type disks to these common mergers and show that thin disks do not survive the bombardment. The remnant galaxies are roughly three times as thick and twice as kinematically hot as the observed thin disk of the Milky Way. Finally, we evaluate the suggestion that disks may be preserved if the mergers involve gas-rich progenitors. Using empirical measures to assign stellar masses and gas masses to dark matter halos as a function of redshift, we show that the vast majority of large mergers experienced by 1012M⊙ halos should be gas-rich (fgas > 0.5), suggesting that this is a potentially viable solution to the disk formation conundrum. Moreover, gas-rich mergers should become increasingly rare in more massive halos > 1012.5M⊙, and this suggest that merger gas fractions may play an important role in establishing morphological trends with galaxy luminosity.