We present new abundance measurements for eleven GCs in the Local Group galaxies NGC 147, NGC 6822, and Messier 33. These are combined with previously published observations of four GCs in the Fornax and WLM galaxies. The abundances were determined from analysis of integrated-light spectra, obtained with HIRES on the Keck I telescope and with UVES on the VLT. We find that the clusters with [Fe/H]<-1.5 are all alpha-enhanced at about the same level as Milky Way GCs. Their Na abundances are also generally enhanced relative to Milky Way halo stars, suggesting that these extragalactic GCs resemble their Milky Way counterparts in containing significant fractions of Na-rich stars. For [Fe/H]>-1.5, the GCs in M33 are also alpha-enhanced, while the GCs that belong to dwarfs (NGC 6822 SC7 and Fornax 4) have closer to Solar-scaled alpha-element abundances, thus mimicking the abundance trends observed in field stars in nearby dwarf galaxies. The abundance patterns in SC7 are remarkably similar to those in the Galactic GC Ruprecht 106, including significantly sub-solar [Na/Fe] and [Ni/Fe] ratios. In NGC 147, the GCs with [Fe/H]<-2.0 account for about 6% of the total luminosity of stars in the same metallicity range, a lower fraction than those previously found in the Fornax and WLM galaxies, but substantially higher than in the Milky Way halo.