I think the one show that always kept me laughing was the Office, and that was mostly because each episode was just a new skit or situation, and not a continuation of the last in most cases. Despite that the characters were persistent and there was a backstory (no matter how silly it was at times). 

One particular idea for a show I read once that had me intrigued was a show where every episode is a completely unrelated story, with the next episode not even mentioning the characters in the last. That would last an entire season with basically a new episode being it's own story and basically being it's own show. Then in the season finale, the episode would reveal that all episodes were connected somehow and that they were chronological too, so ep. 1 caused ep. 2 and so on. I think that'd be amazing to watch even though the concept sounds strange as hell and definitely wouldn't gather a lot of attention at first.

And I shall stop mucking up your thread now then. :lol