If there's any iconic television show that largely aired in the pre-internet era that would lend itself to the modern world, it's The Simpsons. So, it's welcome news that with the show's move in syndication to FXX, The Simpsons will be available for streaming online.
Ideally, of course, Fox will take the South Park path and simply post everything online and make it both searchable and embeddable. But let me propose something a little more radical than the clip database Slate suggested.
I want a special kind of clip database that allows the user to select her own clips from larger episodes, with the ability to embed or link to those edited clips. That is, if I'm watching "Last Exit to Springfield", I want to be able to select a clip as long as Lisa's entire song about the cooling towers or a clip as short as the random dude yelling, "Dental plan!", and put it in its own embeddable video module.
As far as I know, no service does this, but anything is possible.
(Image cc-licensed: "The Simpsons in Springfield" by Cindy Funk)