Globular clusters show abundance variations for light elements that are not yet well understood. The preferred explanation involves a self-enrichment scenario, with two subsequent generations of stars. Observations of main sequence stars allow us to investigate the signature of this chemically processed material without the complicating effects of internal mixing. Our goal is to investigate the C-N anti-correlation with low-resolution spectroscopy of 20-50 stars fainter than the first dredge-up in seven globular clusters (NGC288, NGC1851, NGC5927, NGC6352, NGC6388, and Pal12) with different properties. We complemented our observations with 47~Tuc archival data, with four additional clusters from the literature (M15, M22, M55, NGC362), and with additional literature data on NGC288. In this first paper, we measured the strength of CN and CH band indices, and we investigated the anti-correlation and bimodality of these indices. We compared r_CN, the ratio of stars belonging to the CN-strong and weak groups, with 15 different cluster parameters. We clearly see bimodal anti-correlation of the CH and CN band stregths in the metal-rich clusters (Pal12, 47Tuc, NGC6352, NGC5927). Only M15 among the metal-poor clusters shows a clearly bimodal anti-correlation. We found weak correlations (sligthly above 1 sigma) of r_CN with the cluster orbital parameters, present-day total mass, cluster concentration, and age. 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.

18 pages, 10 figures, 1 electronic table, accepted for publication in A&A (language edited version)