A remarkable percentage of acute gastroenteritis cases remain etiologically undiagnosed. The aim of the study was to determine the prevalence of common and emerging enteric viruses, such as novel human astroviruses, among undiagnosed samples from children with acute gastroenteritis. Epidemiological studies for novel human astroviruses are still scarce. Stool samples collected over two consecutive winter seasons (2016–2017) from children with gastroenteritis in Spain, which were negative for bacteria, rotavirus, and adenovirus by routine diagnostics were screened by real-time RT-PCR assays for the presence of classical and novel astrovirus, rotavirus, norovirus GI and GII, sapovirus, and adenovirus. Overall, 220/384 stool samples (57.3%) were positive for at least one virus. Co-infections were identified in 21% of cases. Among a total of 315 viruses identified, adenovirus was the most prevalent (n = 103), followed by rotavirus (n = 51), sapovirus (n = 50), classical astrovirus (n = 43), novel astroviruses (n = 42), and norovirus (n = 26). Novel astroviruses were present in 13.3% of virus-positive cases. Most novel astroviruses were found in children <2-year-old (30/39 children, 77%, p = 0.01) and were found in co-infection (66%). Only classical astroviruses demonstrated significant differences in the Cq values during mono-infections compared to co-infections. In conclusion, common enteric viruses may be frequently found in children with undiagnosed gastroenteritis, indicating the need to implement more sensitive diagnostic methods. Novel astroviruses circulate in the community and could be the cause of gastroenteritis among young children.