I keep watching The New Adventure of Old Christine in re-runs. For some reason, I can never get into sit-coms until after they're off the air and in syndication.
The kid in it is central to the premise of the show. He's the reason Christine is in constant contact with her ex-husband and his girlfriend, also named Christine. The kid is the reason Christine has to deal with the mean, wealthy moms at his high-priced private school. He's the reason her brother lives with her---he babysits.
But the kid has nothing to do on the show. I don't know if the writers considered this a running gag, but in each episode, Ritchie comes in, says something, and his mother tells him to go upstairs and change, or go to his room, or go take a bath. They don't even try to come up with a good reason why Ritchie has to leave the room. In one episode, they visit Christine's mother.
"Can I go play in the basement?" Ritchie says.