Agent Scully: To a point. In Crystal Skull, Indy is a big skeptic about the existence of alien races, and in Raiders, considers the Ark of the Covenant nothing but a fancy gold box, but when the Ark is opened at the end of the film he insists that he and Marion avert their eyes.
He seems to have little qualms killing if the situation requires it and has shown many times to be a dirty fighter.
There's also the fact he did pretty unmentionable things to an underage Marion Ravenwood (although he maintains that Marion was old enough to know full well what they were doing and give consent). In the original script of The Radiers he's also prone to fooling around with some of his college student.
Arbitrary Skepticism: Despite the fact that he's encountered many powerful artifacts over the years, he still sneers at the prospect of magical telepathic skulls or any new "mystical" discovery.
Berserk Button: One of the few ways to truly enrage the normally logical Henry Jones Junior is to harm an innocent child... just ask the shredded remains of Mola Ram in the bellies of a dozen satisfied crocodiles.
Disappeared Dad: Indy complained that his father was more concerned about artifacts in a museum than his own son. Notably, however, it was Indy that walked out on him.
Disney Death: Similar to Basil from The Great Mouse Detective. In The Last Crusade Indy seems he's fallen to his death in a deep chasm along with Vogel. While his father, Brody, and Sallah peering over the cliff, believing that he died, Indy climbs onto the cliff edge, revealing he's jumped from the tank before it fell..
Iconic Outfit: He does wear a wide variety of clothes in the films but He just isn't Indy without the Leather Jacket and fedora.
I Know Karate: Young Indiana Jones has shown proficiency in Northern Style Kung Fu in his TV series; though this is not retconned into the movie series proper, Indy has consistently been shown to be skilled in US Marines CQC (Close Quarters Combat, made famous by The Boss and Big Boss) since Temple of Doom; justifiable considering his extended experience in the military.
Line-of-Sight Name: "Henry Defense" came into being when he was asked to give a name while enlisting for the Belgium Army in World War I, and the French word "Defense' just happened to be on a plate resting on the desk.
Omniglot: Latin, Greek, Japanese, German, Mayan, Egyptian, French, Spanish, Arabic, Mandarin, Cantonese, Irish, Vietnamese, Hungarian, Hindi, Dutch, Old English, Quechua, American Sign Language, and most likely others. Word of God says he speaks 27 languages. Unfortunately, he didn't take that summer course in Hovitos...
This trope largely came about in the sequelfilms; in Raiders, scriptwriter Lawrence Kasdan intended Indy to be a rather poor hand with foreign languages (which is why he needs someone else to translate the Staff of Ra headpiece inscription).
Only Known by Their Nickname: All of his friends consistently refer to him as "Indiana" or "Indy". It wasn't until the third movie that people learned his first name is actually Henry, and that he got his nickname from their dog.
Sallah: What does it mean, this "junior"?
Henry: That's his name. Henry Jones, Junior.
Indy: I like Indiana.
Henry: We named the dog "Indiana"!
Sallah: You are named after a dog?!
Indy: I've got a lot of fond memories of that dog!
Papa Wolf: "They're innocent children... Mola Ram, prepare to meet Kali IN HELL!!"
And of course, to Mutt. When he thinks that Mutt is simply Marion's son, Indy looks out for him like anyone else with him on an adventure, but when he learns the truth, the trope is embodied full-on.
Ms. Fanservice: In The Raiders especially in her white dress and bare feet. Even in The Crystal Skull she hasn't lost her beauty.
Took a Level in Badass: She starts out capable enough, but grows more and more confident as Raiders goes on, and by the time Kingdom rolls around, she's casually driving amphibious trucks off of cliffs to escape pursuers.
In Crystal Skull, during a heated argument with Indy, he comments that all the women he has been involved with since Marion had one problem, "They weren't you, honey". Cue Marion immediately grinning like a school-girl.
Beware the Nice Ones: He's a nominal christian who doesn't approve Indy's methods like killing. Then he makes a nazi plane crash and blows up an entire tank full of nazi soldiers simply justifying that "It's war !"
Bus Crash: He's mentioned in the fourth film to have died sometime after the third. Justified since Sean Connery refused to come out of retirement just to make some cameo that would ultimately be insignificant.
Took a Level in Dumbass: In Raiders, Sallah was competent, brave and intelligent. In Last Crusade, he was a borderline idiot savant comic relief character whose only redeeming characteristic was he could hit really hard.
Professor Marcus Brody, Dean of Marshall University's Department of Archaeology.
Sallah: (smiles to the bad guys) Papers? Of course... (to Marcus) Run.
Marcus: (stands around looking clueless) ...Yes?
Sallah: Papers. (takes out a newspaper) Got it here. Just finished reading it myself... (trying to provide cover for an escape) Run...
Marcus: (STILL clueless) ...Yes?
Sallah: "Egyptian Mail," morning edition. (exasperated, to Marcus) Run!
Marcus: Did you say, uh...
Sallah: (yelling) RUN!
Took a Level in Badass: Though in the first movie he lamented that if he was as young as Indy he would have went on his adventure. Though most people who seen Crusade have labeled him a clumsy oaf that got lost in his own museum; he was willing to put his complaint in Raiders aside to help Indy rescue Henry. He even had enough cojones to knock a Nazi out with an Artillery shell.
Wilhelmina "Willie" Scott
Aren't You Going to Ravish Me?: Willie during the entire scene where Indy bursts into her room to look for the secret entrance to Kali's temple. "I'm right here!"
Defrosting Ice Queen: Interviews with Spielberg indicate she was meant to be this trope. Unfortunately, she didn't come off this way to most viewers.
Glass Cannon: While he's good with a sword, knife and any improvised weapon. His skills in hand to hand combat vary. He can take on any mook, but when faced in a hand to hand situation with Spalko, she wipes the floor with him.
Heroic Bastard: When he was born, his REAL parents were most certainly NOT married.
Dragon-in-Chief: Nominally the main antagonist of the film, it's actually Nazi Colonel Dietrich who is the one in charge of the quest of the Ark and the one who calls all the shots. However, Belloq uses his smooth talk and archeological expertise to sway Dietrich around to his point of view and get the colonel to do what he wants.
Even Evil Has Standards: Draws the line at rough treatment of women. René repeatedly tries to shield Marion from harm, though he's not overly enthusiastic about it.
A God Am I: You'd almost think René got into this business just so he could hold idols over his head and make people bow to him.
Irony: If it weren't for the test he suggested that ultimately resulted in his and his co-villains Karmic Death on a remote island and delivered it to Berlin as is, there most likely would not have been a World War II because of the Ark blowing it up.
Loveable Rogue: Tries to present himself as this to Marion, and succeeds at first. This illusion is probably shattered for good later when a captured Marion gets shoved around by a soldier and Belloq coldly brushes by without a word.
Manipulative Bastard: Gets into the heads of and manipulates the natives of South America, Marion, and even Indy himself.
Necessarily Evil: What Belloq sees working with the Nazis as. He honestly doesn't give a damn about the Third Reich, he only cares about the money and glory of finding the Ark.
Even Evil Has Standards: Does a very minor one when he seizes the smuggling ship. Captain Katanga tries to protect Marion by implying that he plans to sell her as a Sex Slave, hoping that after the Nazis get their cargo back and find no trace of Indy they'll be satisfied. Instead a visibly disgusted Dietrich immediately grabs Marion and threatens to sink Katanga's ship.
The Stoic: Indiana Jones hijacking the truck carrying the Ark and all the wild driving his Mercedes is put through as a result? It barely earns a raised eyebrow and a mild frown from him.
Not So Stoic: Although Indy continually coming out of nowhere to ruin his mission eventually starts getting to him, both with the tossing a melon at a dog thing and when his men can't find Indy on the smuggler's ship. "WHAT ABOUT JONES?!!"
Wicked Cultured: Listens to a record player and drinks bourbon from a cut crystal decanter outside his tent in Tanis.
We Have Reserves: At one point he instructs a mook to shoot both Indy and another mook who are in the middle of wrestling for possession of a gun. Backfires spectacularly, since now Indy and said mook both want to shoot the same guy with the gun.
Brainwashed and Crazy: The shooting script and novelization had Mola Ram have the same confused and bewildered, snapping-out-of-brainwashing reaction as everyone else that was mind-controlled after handling the glowing stone. In those version he looks confused and terrified for a second, then falls to the crocodiles. The final film, however, does not have this.
Affably Evil: Out of all of Indy's foes, she treats him with the most respect and as an equal. She also showed genuine horror and sadness at the death of Dovchenko, implying that she saw the fellow colonel as a friend rather than just a tool.
I Know Karate: According to Cate Blanchett, Irina knows Shotokan-Ryu Karate to be exact. However, considering Irina's vocation as a Russian soldier, its more likely to be the Soviet Military art of Sambo.
I Know Karate: Specifically, the Russian Military martial art of Sambo, which focuses on throws, grappling and painful joint-locks/breaks. Combined with his already impressive size and strength, Dovchenko's mastery of Sambo almost allowed him to kill Indy were it not for the timely presence of a tree branch...
Mighty Glacier: Though relying more on technique and skill rather than brute force alone.