We present Lick line-index measurements of extragalactic globular clusters in seven early-type galaxies (NGC 1380, 2434, 3115, 3379, 3585, 5846, and 7192) with different morphological types (E-S0) located in field and group/cluster environments. High-quality spectra were taken with the FORS2 instrument at ESO's Very Large Telescope. similar to 50% of our data allows an age resolution Delta t/t approximately 0.3 and a metallicity resolution similar to 0.25-0.4 dex, depending on the absolute metallicity. Globular cluster candidates are selected from deep B, V, R, I, K FORS2/ISAAC photometry with 80-100% success rate inside one effective radius. Using combined optical/near-infrared colour-colour diagrams we present a method to efficiently reduce fore-/background contamination down to 10%. We find clear signs for bi-modality in the globular cluster colour distributions of NGC 1380, 3115, and 3585. The colour distributions of globular clusters in NGC 2434, 3379, 5846, and 7192 are consistent with a broad single-peak distribution. For the analysed globular cluster systems the slopes of projected radial surface density profiles, of the form capital sigma (R) similar to R super(- Gamma ), vary between similar to 0.8 and 2.6. Blue and red globular cluster sub-populations show similar slopes in the clearly bi-modal systems. For galaxies with single-peak globular cluster colour distributions, there is a hint that the blue cluster system seems to have a more extended radial distribution than the red one. Using globular clusters as a tracer population we determine total dynamical masses of host galaxies out to large radii ( similar to 1.6-4.8 R sub(eff)). For the sample we find masses in the range similar to 8.8 x 10 super(10) M. up to similar to 1.2 x 10 super(12) M. The line index data presented here will be used in accompanying papers of this series to derive ages, metallicities and abundance ratios. A compilation of currently available high-quality Lick index measurements for globular clusters in elliptical, lenticular, and late-type galaxies is provided and will serve to augment the current data set.