  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 (<r_CN>=0.82+/-0.29), as
opposed to results based on the Na-O anti-correlations.
