Context. Globular clusters show star-to-star abundance variations for light elements that are not yet well understood. The preferred explanation involves a self-enrichment scenario, within which two subsequent generations of stars co-exist in globular clusters. Observations of chemical abundances in the main sequence and sub-giant branch stars allow us to investigate the signature of this chemically processed material without the complicating effects caused by stellar evolution and internal mixing. Aims: Our main goal is to investigate the carbon-nitrogen anti-correlation with low-resolution spectroscopy of 20-50 stars fainter than the first dredge-up in seven Galactic globular clusters (NGC 288, NGC 1851, NGC 5927, NGC 6352, NGC 6388, and Pal 12) with different properties. We complemented our observations with 47 Tuc archival data, with four additional clusters from the literature (M 15, M 22, M 55, NGC 362), and with additional literature data on NGC 288. Methods: In this first paper, we measured the strengh of the CN and CH band indices, which correlate with the N and C abundances, and we investigated the anti-correlation and bimodality of these indices. We compared rCN, the ratio of stars belonging to the CN-strong and weak groups, with 15 different cluster parameters. Results: We clearly see bimodal anti-correlation of the CH and CN band stregths in the metal-rich clusters (Pal 12, 47 Tuc, NGC 6352, NGC 5927). Only M 15 among the metal-poor clusters shows a clearly bimodal anti-correlation. We found weak correlations (sligthly above 1σ) of rCN with the cluster orbital parameters, present-day total mass, cluster concentration, and age. Conclusions: Our findings support the self-enrichment scenario, and suggest that the occurrence of more than two major generations of stars in a GGC should be rare. Small additional generations (<10-20% of the total) would be difficult to detect with our samples. The first generation, which corresponds to the CN-weak stars, usually contains more stars than the second one ( = 0.82±0.29), as opposed to results based on the Na-O anti-correlations. Based on FORS observations collected at the European Southern Observatory, Chile, within the observing programs 68.D-0510 and 69.D-0056. Also based on data obtained from the ESO Archive, within the observing program 67.D-0153.Complete Table 2 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/524/A44