(or "And Then The Children Were Rescued By...Oh, Let's Say Moe.")
The storytelling engine of the Simpson family is a pretty familiar one to anyone who watches television. The average family with a not-so-average life is pretty familiar ground for television comedy, and has been ever since the days of 'I Love Lucy'. Matt Groening (who supposedly based the series on his own family) created a deceptively simple family structure that generates plenty of stories--the dumb-but-loveable dad, the mischievous-but-good-at-heart son, the intelligent-but-socially-awkward daughter, and the slightly-stir-crazy stay-at-home mom each have their own reasons to provide the writer with storylines (and hyphens, apparently.) Groening's main contribution to the genre was to open up the throttle slightly in a way that works well with the choice of cartoons as a way to deliver the series. Homer isn't just dumb, he's cartoonishly stupid. Bart isn't just mischievous, he's cartoonishly wicked, et cetera, et cetera.
The series developed the other elements of its storytelling engine over its first few seasons, bringing in supporting characters like Moe and Barney, settings like the nuclear power plant and the school, and gradually developing more ways to generate stories as it went on. This is pretty much par for the course with any sitcom (although as a cartoon, the Simpsons have the advantage of not having to worry about actor availability. You can develop a much larger supporting cast when they're all really Hank Azaria.) Again, this is nothing we haven't seen in any sitcom.
But all family sitcoms suffer from the same problem--there's only a limited number of stories you can tell that don't fundamentally break the status quo (and let's not forget, the "status quo" is simply the set of elements making up the current storytelling engine.) One of the key elements of a family sitcom is that in the end, despite the wacky adventures, the family finds a way to put things right at the end of every episode. The more wild the adventure, the harder it is to put things right, and so eventually sitcoms falter as they run out of new wacky adventures.
Which is where the Simpsons broke ranks, back in Season Five. Oh, sure, they'd had a few adventures that were a little outrageous, ones that maybe stretched the limits of the audience's belief that things would really be "back to normal", but the episode 'Homer Loves Flanders' marked a real departure in the series' whole direction. In it, Homer becomes best friends with annoying goody two-shoes Ned Flanders, and at the end of the episode, nothing occurs to break up their friendship. Indeed, they deepen their mutual respect for each other in the episode's climax, prompting Lisa to comment, "Is this the end to our wacky adventures?"
And then the episode ends with a coda, where "next week", Homer hates Flanders as if nothing had ever happened. From that point on, the Simpsons operates on the assumption that unless a future episode explicitly mentions a change to the status quo, it's assumed that everything simply resets back to the default state. So Apu and Manjoula really get married, because she shows up in later episodes, but Bart and Lisa don't wind up trapped on a desert island along with the whole class of Springfield Elementary.
This is a whole new kind of idea, a post-modern take on the storytelling engine that takes it for granted that the audience is not only familiar with the storytelling engine of the Simpsons, but the concept of a storytelling engine in general and the way that a sitcom works. It allows the writers much more creative freedom than the traditional sitcom--they don't have to come up with an ending that returns everything to normal, they just have to take their ideas as far as they can logically go, and let the audience's knowledge of the "sitcom rules" do the rest. Arguably, the series has overused the idea a bit, as it moves on into its twentieth season, but then again, the very fact that it even has a twentieth season, when such legendary sitcoms as 'The Cosby Show' and 'All In the Family' didn't even run for half that length, shows that the Simpsons' elasticity is one of the overlooked elements to their long-running sucess.