With the availability of increasing amounts of genomic sequences, it is becoming clear that genomes experience horizontal transfer and incorporation of genetic information. However, to what extent such horizontal gene transfer (HGT) affects the core genealogical history of organisms remains controversial. Based on initial analyses of complete genomic sequences, HGT has been suggested to be so widespread that it might be the "essence of phylogeny" and might leave the treelike form of genealogy in doubt. On the other hand, possible biased estimation of HGT extent and the findings of coherent phylogenetic patterns indicate that phylogeny of life is well represented by tree graphs. Here, we reexamine this question by assessing the extent of HGT among core orthologous genes using a novel statistical method based on statistical comparisons of tree topology. We apply the method to 40 microbial genomes in the Clusters of Orthologous Groups database over a curated set of 297 orthologous gene clusters, and we detect significant HGT events in 33 out of 297 clusters over a wide range of functional categories. Estimates of positions of HGT events suggest a low mean genome-specific rate of HGT (2.0%) among the orthologous genes, which is in general agreement with other quantitative of HGT. We propose that HGT events, even when relatively common, still leave the treelike history of phylogenies intact, much like cobwebs hanging from tree branches.