We present uniformly measured star formation histories (SFHs) of 60 nearby (D~4Mpc) dwarf galaxies based on CMDs of resolved stellar populations from images taken with HST as part of the ACS Nearby Galaxy Survey Treasury program (ANGST). This volume-limited sample contains 12 dSph/dE, 5 dwarf spiral, 28 dI, 12 transition, and 3 tidal dwarf galaxies. From the best fit SFHs we find three significant results: (1) the average dwarf galaxy formed >50% of its stars by z~2 and 60% of its stars by z~1, regardless of current morphological type; (2) the mean SFHs of dIs, dTrans, and dSphs are similar over most of cosmic time, with the clearest differences appearing during the most recent 1 Gyr; and (3) the mean values are inconsistent with simple SFH models, e.g., exponentially declining SFRs. The mean SFHs are in general agreement with the cosmic SFH, although we observe offsets near z~1 that could be evidence that low mass systems experienced delayed star formation relative to more massive galaxies. The sample shows a strong density-morphology relationship, such that the dSphs are less isolated than dIs. We find that the transition from a gas-rich to gas-poor galaxy cannot be solely due to internal mechanisms such as stellar feedback, and instead is likely the result of external mechanisms, e.g., ram pressure and tidal forces. The average transition dwarf is slightly less isolated and less gas-rich than the typical dI. Further, the transition dwarfs can be divided into two groups: interacting and gas-poor or isolated and gas-rich, suggesting two possible evolutionary pathways. ; Comment: Submitted to ApJ; 32 pages, 16 Figures