"What is it about Mario that's so goddamn enduring?" To answer that question we should first ask another related question: "Why is that Mario — and not Luigi — is so enduring as a character?" Comparing Mario to Luigi seems a strange way to frame a discussion about Mario, but I think that by just highlighting one difference between the two brothers we will be able to answer the first question.
I ask the second question because Luigi, more so than Mario, fits into the archetype of what a video game hero 'should be'. For instance, whereas Luigi is tall and skinny, Mario is short and portly; and in either case, both Mario and Luigi are a far cry from the hyper-masculine heroes that have dominated and continue to dominate gaming. However, I think it is precisely this fact that has made Mario stand the test of time. Although I can't speak for everyone that reads this site and that plays video games, I imagine that like myself, most gamers are more Mario than Nathan Drake. That is, few of us here are handsome and charming rogues like Drake. Yet, despite his physical short comings, Mario, a lowly, short, mustachioed, frankly overweight plumber through his heroics manages to gain time and again the love and affection of a beautiful princess. Suffice to say, despite my best attempts I have yet to find my beautiful princess, but Mario's example gives me hope that maybe one day I too will find my own 'princess'. Until that day I have Mario to uphold my faith that anything is possible, and that the 'little guy' does in fact win from time to time.
I imagine that most who tried to answer the above question likely focused on the simple but ingenious gameplay of the Mario games, and explored how effortlessly that gameplay has transitioned from the realm of 2D to 3D. Those that took that route are, of course, right. After all, a game is nothing without fun gameplay. However, the fact that I, along with others, can engage with Mario and his games in a variety of ways speaks volumes about why Mario has been so enduring. Finally, I want to finish by leaving you with a thought: despite what the cynics say about video gaming, I think it says a lot about our chosen form of entertainment when one of the most recognizable heroes is a less-than-ideal Italian plumber. What other medium can make a similar claim?