Gene expression is controlled by regulatory elements within accessible chromatin. Although most regulatory elements are cell type-specific, a subset is accessible in nearly all the 517 human and 94 mouse cell and tissue types assayed by the ENCODE consortium. We systematically analyzed 9000 human and 8000 mouse ubiquitously-accessible candidate cis-regulatory elements (cCREs) with promoter-like signatures (PLSs) from ENCODE, which we denote ubi-PLSs. These are more CpG-rich than non-ubi-PLSs and correspond to genes with ubiquitously high transcription, including a majority of cell-essential genes. ubi-PLSs are enriched with motifs of ubiquitously-expressed transcription factors and preferentially bound by transcriptional cofactors regulating ubiquitously-expressed genes. They are highly conserved between human and mouse at the synteny level but exhibit frequent turnover of motif sites; accordingly, ubi-PLSs show increased variation at their centers compared with flanking regions among the approximately 186 thousand human genomes sequenced by the TOPMed project. Finally, ubi-PLSs are enriched in genes implicated in Mendelian diseases, especially diseases broadly impacting most cell types, such as deficiencies in mitochondrial functions. Thus, a set of roughly 9000 mammalian promoters are actively maintained in an accessible state across cell types by a distinct set of transcription factors and cofactors to ensure the transcriptional programs of cell-essential genes.