Adenoviruses are important human pathogens that have been developed as vectors for gene therapies and genetic vaccines. Previous studies indicated that human infections with adenoviruses are self-limiting in immunocompetent hosts with evidence of some persistence in adenoid tissue. We sought to better understand the natural history of adenovirus infections in various non-human primates and discovered that healthy populations of great apes (chimpanzees, bonobos, gorillas, and orangutans) and macaques shed substantial quantities of infectious adenoviruses in stool. Shedding in stools from asymptomatic humans was found to be much less frequent, comparable to frequencies reported before. We purified and fully sequenced 30 novel adenoviruses from apes and 3 novel adenoviruses from macaques. Analyses of the new ape adenovirus sequences (as well as the 4 chimpanzee adenovirus sequences we have previously reported) together with 22 complete adenovirus genomes available from GenBank revealed that (a) the ape adenoviruses could clearly be classified into species corresponding to human adenovirus species B, C, and E, (b) there was evidence for intraspecies recombination between adenoviruses, and (c) the high degree of phylogenetic relatedness of adenoviruses across their various primate hosts provided evidence for cross species transmission events to have occurred in the natural history of B and E viruses. The high degree of asymptomatic shedding of live adenovirus in non-human primates and evidence for zoonotic transmissions warrants caution for primate handling and housing. Furthermore, the presence of persistent and/or latent adenovirus infections in the gut should be considered in the design and interpretation of human and non-human primate studies with adenovirus vectors.