King of the Hill is a great example of a slice-of-life show. The conflicts introduced in each episode are usually pretty dang believable, can be resolved by the characters being honest and/or actually opening up about their feelings, and feels grounded in a way no other animated show (and few live action shows for that matter) could be.

Heck, one of the better episodes of season 1 is about Hank Hill being constipated because of his stubborn refusal to change his diet or ask for help. It seems like a silly premise for a 23 minute episode, but it's so relatable that it works.