(or "Know Thyself")
Indiana Jones' storytelling engine was worked out by two absolute masters of their form while both of them were (arguably) at their creative peak, and it shows. (Yes, let's just get the gushing out of the way now.) It's a brilliant idea, one that's so great that it was either ahead of its time or else just copied a lot--take a particular era (such as the 1930s), and then take the tropes of its fiction and apply them as though the era really was like that. So just as Doctor Who pastiched the fictional image of Victorian London in "The Talons of Weng-Chiang" instead of using the much duller actual London (hey, Doctor Who has always been ahead of its time, even for a time-travel show), George Lucas and Steven Spielberg decided to create a two-fisted pulp image of the times leading into World War II and make it seem real.
Part and parcel of this was their brilliant (again, gushing) decision to treat myths and legends as real (within the context of the entirely unreal 1930s they'd created for the series.) In the world of Indiana Jones, all the ancient relics and mysterious MacGuffins of all those pulps really did what they said they did, and a daring treasure hunter (let's face it, the "archaeology" thing is just a dodge) has to clash just as much with the supernatural as he does with fiendish death traps, cold-hearted Nazi seductresses, and decidedly unfriendly natives. (Which remains a problematic element for any story that pastiches the fictional tropes of another time--do you use story elements that have not aged well in terms of their racism and sexism, and hope that your audience is well-educated enough to understand the context of their usage, or do you eliminate them, cutting out a lot of the authenticity of your pastiche?)
So what we have in your basic Indiana Jones story, as generated by the engine, is a story set in the era of the pulps, using tropes and stock characters/settings generated by them, with supernatural elements usually added in (but not necessarily required)...and then overlaying that with a veneer of authenticity by a) researching the historical myths that are the basis for the supernatural elements (you'd be amazed at just how much work went into getting the bits about the Ark of the Covenant as close to "right" as they could), and b) having a lead character who's flawed and human in a way that pulp heroes tended not to be. (Anyone see Doc Savage whimpering in pain and saying, "It's not the years, it's the mileage?") And yet, it's important to note that for all of Indy's flaws, he's flawed in a human, likeable way. His original motivation for treasure hunting (he's a playboy professor who lives beyond his means and sells his finds to finance his lifestyle) is almost totally muted in the series as we see it on screen...and in books, comics, video games, et cetera.
Just a quick sampling of the books, comics, video games, et cetera bears this out. We see Indy searching for the fourth nail of Christ's cross, fighting zombi armies in Haiti, searching for Atlantis and the supposed lands inside a hollow Earth, fighting dragons, and duking it out with Tibetan telekinetics. He even met Dracula. This seems like a very sustainable engine.
So why is it that audiences seem so reluctant to embrace Indy's sequels? (For a given value of "reluctant"--it's not like the Indy movies don't make money.) Setting aside the books and comics and video games for the moment--those tend to be produced for the "fan", not the casual enthusiast--only two of the four movies have gotten a good critical response, and the "Young Indiana Jones" television series crashed and burned after just two seasons, a genuine shocker considering the high-profile talent working on it. The fourth movie, in particular, was thoroughly panned (despite, again, not having any problems making money.)
Looking at the movies that were loved and the ones that were merely tolerated, it's easy to spot why--just look for the ones that didn't use the storytelling engine. 'Indiana Jones and the Temple of Doom' skimped on its research, making up its MacGuffin (and not incidentally, falling on the wrong side of the "problematic" question mentioned above...all too often, it seems to use its pulp tropes as an excuse for racism, rather than attempting to examine the attitudes of the era it pastiches.) "Young Indiana Jones" skimps on the adventure--apart from one episode where Indy meets Dracula, most of the stories revolved around boringly educational meetings with historical figures and tame escapades in historical settings. There's no zip to them.
And 'Kingdom of the Crystal Skull'...the fourth Indiana Jones movie essentially tries to invent a brand-new storytelling engine built on the principles of the original, but using the tropes of 50s science-fiction films instead of 30s pulp films. Which is an interesting idea, and one that almost becomes necessary in order to continue using Harrison Ford as Indy (and let's face it, Ford's performance is 90% of what makes the character who he is; none of the other actors have ever managed to make the character work quite so well.)
But back when they were first considering the idea, Lucas and Spielberg had the option to use any era they wanted, and they chose the pulps of the 30s over the sci-fi 50s. Perhaps it was that Nazis made better bad guys than commies, perhaps it was because ancient relics were more exciting than flying saucers, perhaps it was just because Crash Corrigan was more fun than Flash Gordon, but for whatever reason, they saw that one era had more potential than the other for stories. Setting aside any question of whether Lucas and Spielberg have "lost it" over the decades, the storytelling engine they made the first time just worked in a way that the new one doesn't, which doesn't exactly bode well for attempts to make a fifth Indiana Jones movie. But the fundamental soundess of the original storytelling engine means that Indy books and comics, at least, can keep going strong for ages to come.