I've had this discussion several times with many different people, but I figured that it deserved a deeper delving than I'd been giving it (or maybe it doesn't, but I'm going to do so anyway).
Indiana Jones is a murderer. Bottom line. I mean, we as an audience can justify to ourselves all of the different reasons why he had to kill this person or that, but the fact remains that he's running all over the globe in search of these artifacts, and he's killing anyone along the way that tries to stop him. Why is he the righteous collector, and all of the others are criminals or villains? Look at The Last Crusade; Indy steals - literally steals - the Cross of Coronado from the archeological expedition, and then he gets pissed when the guy brings the police to retrieve the stolen goods. I mean, what do you expect, Indy?
In the first movie, Raiders of the Lost Ark, we're supposed to feel bad for Indy for getting the golden monkey head stolen, first by his guide (played by a young Alfred Molina), and then by Belloq along with the help of the Hovitos. If Indy would have thought to learn Hovitos, and then solicit the help of the indigenous tribe, he would have done so. Belloq was just one step ahead of him.
A glaring example of Indy's disregard for human life is in the market in Cairo. Marion has been taken, and Indy is looking for her. He runs through the market knocking over any and all baskets looking for Marion, completely oblivious to the fact that he's pissing everyone off. Then, we have a man with a Scimitar challenge Indy to a fight (with some waving of the sword). Indy just pulls his gun out and murders the man in cold blood. In fact, he gets kind of a cool smirk on his face, like he's a badass for doing so, when, in fact, he's just cold-blooded.
Then we have Indy out at the Tanis excavation, and here is where the dude truly goes off (as does Marion). Listen, I know that the Nazi's were awful, and therefore there's little pity for some dead Nazi's, but that still doesn't mean that some sociopathic archaeologist can just murder them by the handful without any consequences. I mean, they are people, right? But he goes out to find the ark, and once they're onto his game, he decides he needs to bail, and kills anyone in his way to do so.
In the third movie dude is killing Nazis all over the place. In the castle, on the road, in the desert, on a tank. Indy is just a straight up killer, and not only a Nazi killer, but a killer of anyone that will stand between him and his rare antiquities. I guess I could forgive the Nazi killing for a second if it wasn't problematic to me that Indy seems to be completely remorseless for killing anyone, and never stops to make sure that he's killed the right or wrong person, and it never comes back to him that he has killed so many people - he's emotionless about it. Not to mention the fact that the guy is a globetrotting murderer, and yet he never seems to have any problems with the law, or create some sort of international incident, even though he's killing citizens from many countries scattered throughout the world.
Added to the fact that he's an unrepentant murderer, Indiana Jones is also a womanizer, who treats women like trash. In Raiders, it is revealed that he has been in a previous relationship with Marion, and that he broke her heart. He comes back into her life to find an antiquity (cares nothing about her feelings, or how having not seen him for several years will have affected her), and then once he's collected his antiquity he will be on his way. But his mission is complicated by the fact that she's kidnapped and seemingly killed. He mourns on this over a bottle of alcohol, and then seems perfectly fine as he continued upon his mission to find the ark. Once he finds Marion in a tent, and realizes that she's not dead, he kisses her for about .2 seconds, and then tells her that he can't untie her or help her escape, because then they would know Indy was around, and would prevent him from finding the ark. I mean, dude didn't know what the Nazis had in mind for her. Maybe they were routinely raping her, and they were going to perform medical experiments on her body, and he just leaves her there to deal with whatever they plan on giving her. Then there is some sort of reconciliation at the end, but we realize this is short-lived when Indy shows up in Temple of Doom Marion-less.
In Temple, we have the beautiful wife of Steven Spielberg, Kate Capshaw, playing "Willie", a nightclub singer and dancer who has a penchant for adventurous men and the finer things in life. She gets caught up in the whole mess Indy creates, and he proceeds to treat her like garbage throughout the rest of the movie, and only gives her affection from time to time when either he wants something from her, or he needs to get a little booty. Again, Willie disappears after Temple, never be seen or heard from again.
The most interesting relationship of the trilogy (I don't include The Crystal Skull as a real Indiana Jones movie) is that with Dr. Schneider. Frau Schneider is a very strong woman, and therefore Indy likes her very much. Even after she betrays him, he still tries to save her at the end. But the rest of the movie he's pushing her around, yelling at her, and basically just treating her like a dog.
Bottom line: Indiana Jones cares about nothing and no one but himself.