CRISPR-Cas systems provide prokaryotes with adaptive defense against bacteriophage infections. Given an enormous variety of strategies used by phages to overcome their hosts, one can expect that the efficiency of protective action of CRISPR-Cas systems against different viruses should vary. Here, we created a collection of Escherichia coli strains with type I-E CRISPR-Cas system targeting various positions in the genomes of bacteriophages λ, T5, T7, T4 and R1-37 and investigated the ability of these strains to resist the infection and acquire additional CRISPR spacers from the infecting phage. We find that the efficiency of CRISPR-Cas targeting by the host is determined by phage life style, the positions of the targeted protospacer within the genome, and the state of phage DNA. The results also suggest that during infection by lytic phages that are susceptible to CRISPR interference, CRISPR-Cas does not act as a true immunity system that saves the infected cell but rather enforces an abortive infection pathway leading to infected cell death with no phage progeny release.