Recent genome-wide experiments in different eukaryotic genomes provide an unprecedented view of transcription factor (TF) binding locations and of nucleosome occupancy. These experiments revealed that a large fraction of TF binding events occur in regions where only a small number of specific TF binding sites (TFBSs) have been detected. Furthermore, in vitro protein-DNA binding measurements performed for hundreds of TFs indicate that TFs are bound with wide range of affinities to different DNA sequences that lack known consensus motifs. These observations have thus challenged the classical picture of specific protein-DNA binding and strongly suggest the existence of additional recognition mechanisms that affect protein-DNA binding preferences. We have previously demonstrated that repetitive DNA sequence elements characterized by certain symmetries statistically affect protein-DNA binding preferences. We call this binding mechanism nonconsensus protein-DNA binding in order to emphasize the point that specific consensus TFBSs do not contribute to this effect. In this paper, using the simple statistical mechanics model developed previously, we calculate the nonconsensus protein-DNA binding free energy for the entire C. elegans and D. melanogaster genomes. Using the available chromatin immunoprecipitation followed by sequencing (ChIP-seq) results on TF-DNA binding preferences for ~100 TFs, we show that DNA sequences characterized by low predicted free energy of nonconsensus binding have statistically higher experimental TF occupancy and lower nucleosome occupancy than sequences characterized by high free energy of nonconsensus binding. This is in agreement with our previous analysis performed for the yeast genome. We suggest therefore that nonconsensus protein-DNA binding assists the formation of nucleosome-free regions, as TFs outcompete nucleosomes at genomic locations with enhanced nonconsensus binding. In addition, here we perform a new, large-scale analysis using in vitro TF-DNA preferences obtained from the universal protein binding microarrays (PBM) for ~90 eukaryotic TFs belonging to 22 different DNA-binding domain types. As a result of this new analysis, we conclude that nonconsensus protein-DNA binding is a widespread phenomenon that significantly affects protein-DNA binding preferences and need not require the presence of consensus (specific) TFBSs in order to achieve genome-wide TF-DNA binding specificity. 