It depends. My immediate response to this question is a resounding “yes,” but then I think about screaming toddlers and hungry infants. Thus, it depends.
When I was growing up and my mother took me to a Baptist church, I sat quietly doodling on tithe envelopes and “scribble cards” a lot. My parents divorced when I was a toddler, and my mother was the only one with a religious preference or an inclination to go to church. Since I visited my father every other weekend, this system meant that I only attended church every other Sunday.
My mother really wanted me to regularly attend Sunday school with kids my age, but since I wasn’t there every week, I felt like the other kids would leave me out. I wasn’t a member of the church we attended nor did I have the ability to attend every Sunday. The few times that I attended, Sunday school felt like another clique I didn’t belong to. It didn’t take me long to start sitting in the pews with my mother, which I enjoyed much more especially when I could sing along with the worship songs. Eventually, I even started listening to the sermons and taking notes (when they offered fill-in-the-blank outlines).
Personally, I think that having the option of kids sitting in service with their parents or going to Sunday school or child care makes for a more accepting and full community. I know not all kids want or need to sit with their parents during worship services, but for me, it was a blessing to be able to. I really appreciate it when churches have sections reserved for families, so that if a child becomes disruptive, a parent can slip out with the child without making too big of a scene. Fellowship between believers is for all ages; after all, Jesus said, “Let the little children come to me” (Matthew 19:14).