Viral co-infections are frequently observed among children, but whether specific viral interactions enhance or diminish the severity of respiratory disease is still controversial. This study aimed to investigate the type of viral mono- and co-infections by also evaluating viral correlations in 3525 respiratory samples from 3525 pediatric in/outpatients screened by the Allplex Respiratory Panel Assays and with a Severe Acute Respiratory Syndrome-COronaVirus 2 (SARS-CoV-2) test available. Overall, viral co-infections were detected in 37.8% of patients and were more frequently observed in specimens from children with lower respiratory tract infections compared to those with upper respiratory tract infections (47.1% vs. 36.0%, p = 0.003). SARS-CoV-2 and influenza A were more commonly detected in mono-infections, whereas human bocavirus showed the highest co-infection rate (87.8% in co-infection). After analyzing viral pairings using Spearman’s correlation test, it was noted that SARS-CoV-2 was negatively associated with all other respiratory viruses, whereas a markedly significant positive correlation (p < 0.001) was observed for five viral pairings (involving adenovirus/human bocavirus/human enterovirus/metapneumoviruses/rhinovirus). The correlation between co-infection and clinical outcome may be linked to the type of virus(es) involved in the co-infection rather than simple co-presence. Further studies dedicated to this important point are needed, since it has obvious implications from a diagnostic and clinical point of view.