We present uniformly measured star formation histories (SFHs) of 40 Local Group (LG) dwarf galaxies based on color-magnitude diagram (CMD) analysis from archival Hubble Space Telescope imaging. We demonstrate that accurate SFHs can be recovered from CMDs that do not reach the oldest main sequence turn-off (MSTO), but emphasize that the oldest MSTO is critical for precisely constraining the earliest epochs of star formation. We find that: (1) the average lifetime SFHs of dwarf spheroidals (dSphs) can be approximated by an exponentially declining SFH with {tau} ~ 5 Gyr; (2) lower luminosity dSphs are less likely to have extended SFHs than more luminous dSphs; (3) the average SFHs of dwarf irregulars (dIrrs), transition dwarfs, and dwarf ellipticals can be approximated by the combination of an exponentially declining SFH ({tau} ~ 3-4 Gyr) for lookback ages >10-12 Gyr ago and a constant SFH thereafter; (4) the observed fraction of stellar mass formed prior to z = 2 ranges considerably (80% for galaxies with M < 10^5^ M_{sun}_ to 30% for galaxies with M > 10^7^ M_{sun}_) and is largely explained by environment; (5) the distinction between "ultra-faint" and "classical" dSphs is arbitrary; (6) LG dIrrs formed a significantly higher fraction of stellar mass prior to z = 2 than the Sloan Digital Sky Survey galaxies from Leitner and the SFHs from the abundance matching models of Behroozi et al. This may indicate higher than expected star formation efficiencies at early times in low mass galaxies. Finally, we provide all the SFHs in tabulated electronic format for use by the community.