Fan since 1981
I've been an Indy fan since Raiders came out. I was ten years old. My much older sister took me to see it. I didn't know what it was so I wasn't in an appreciative mood. While she was dragging me around some shops before the show, she said something that put me in a little sulk and I remember resolving to 'show her' by keeping my eyes shut for the whole film. This revenge plan was of course forgotten as soon as the film began and I was immediately gripped by the mysterious trek through the jungle. And then when we finally saw Indy's face I recognised him as Han Solo.
In my house, growing up, we watched a lot of golden age Hollywood movies, so I recognised how Raiders captured that era in aspects such as lighting techniques and John Williams's score sounding like the scores of that time. In the early 80's, we didn't have much choice on TV in England, just four channels. Old Hollywood movies made up a big part of what everyone watched. I expect that today, and evermore, this frame of reference is lost on a lot of people watching Indy because movies from that era get less and less airing.
One of my favourite movies is The Maltese Falcon.
I always thought that the back story in it sounds just like an adventure Indy would be involved in. The supporting characters - and in my imagination, Indy - in the Far East, each trying to get the Falcon before the others. That the Falcon's value is monetary and it just happens to be a historical artifact, not possessed of supernatural powers, makes it fit my preferred interpretation of Indy, as we find him at the start of Raiders, a 'finder of rare antiquities', using them as a source of finance, fortune and glory. (I am less interested in the Indy we get later who has developed the proper belief that artifacts belong in a museum and only goes adventuring because of family.)
I'd enjoy Indy adventures that have no supernatural elements, just pure treasure hunts with bad guys/rivals who are motivated by greed instead of wanting World Dominating Power. And Indy himself being shadier - to me, he is one of the raiders of the title, which is significant when the title format changes to "Indiana Jones and the *whatever*", reflecting his move more into the light.
But regarding supernatural elements, I also enjoy seeing parallels of Indy in some of the stories of M.R. James. You get the background of academia, the interest in ancient relics and pursuit/discovery of one that turns out to hold terrible powers. I like to imagine Indy in smaller scale, scary stories like these.