Extremely Lengthy Creation: The sequel to the trilogy had been planned for over a decade, but it had to wait for a plot that all the major players (Spielberg, Harrison Ford, etc.) felt was worthy of the title character.
Indy's failed attempt to impersonate a Scottish laird in The Last Crusade is an in-character version, if not a Lampshading of this trope, which originated with Harrison Ford attempting to mimic Sean Connery's accent while playing around.
Hey, It's That Voice!: Does that monkey in Raiders sound like Abu to you? Frank Welker actually got the role in Aladdin on recommendation from Steven Spielberg, who recalled the excellent vocal performance he gave in Raiders.
Real-Life Relative: Isla Blair, Mrs. Julian Glover offscreen, played Mrs. Donovan in Last Crusade.
In Crystal Skull, the girl who punches Mutt in the diner is Sophie Spielberg, daughter of Steven Spielberg and Kate Capshaw (Willie Scott in Temple of Doom).
Refitted For Sequel: Lucas is notorious for just not. letting. go. whatever he has decided should be in the Indy continuity. If money or pacing prevents it from showing up in an installment, it sure will appear in the next.
Temple of Doom included several sequences originally planned for Raiders of the Lost Ark:
Much of the original sword fight that would have been between Indy and the swordsman he shot instead made it into the sword fight at the end of Temple of Doom (where Indy tries the same thing, but his gun is missing).
The minecart chase was originally planned for Raiders (and even storyboarded) but had to be cut for pacing reasons.
Indy visiting Shanghai to retrieve a relic from a powerful local and hiding behind a rolling gong from machine gunfire, as well as the pilots jumping off a plane and Indy escaping in a life raft and down a mountain slope were in the original script for Raiders.
The rolling gong went as far as being storyboarded.
The woman that would become Marion was first envisioned as an old flame of Indy that owned a bar, was a Jazz singer and a double agent for the Nazis. The singer part went to Willie in Doom and the double agent part to Elsa in Crusade.
The first drafts of the third movie had Indy getting in a haunted castle in Scotland. The castle (moved to Austria), the revolving door and even Indy speaking with a poor Scottish accent made it into the final film, but Spielberg didn't want to do another haunted house after Poltergeist. The haunted castle finally showed up in a Young Indy TV episode, Transylvania, January 1918.
The following drafts had Indy retrieving an artifact from an old foe in Mexico, in a scene that payed homage to old Western bar fight scenes. The first episode that (re)introduced teenage Indy in the TV series had a bar fight and Indy retrieving an artifact from a foe made in his childhood (i.e. the previous episode) in Mexico.
Another recurrent idea in these drafts was Indy being attacked by gorillas and then convincing them to turn against his enemies (they were still used in the Mexico prologue, with the enemy using trained gorillas as sidekicks). In Skull, Mutt directs an attack of South American monkeys against the Russians.
An episode of the never produced fourth season of the TV series would have Indy meeting Belloq for the first time and following Percy Fawcett in his (historical) expedition to find a lost city in Brazil. Fawcett later showed up as a secondary character in one of the most important Indy novels, Indiana Jones and the Seven Veils.
Another episode would show the beginning of Indy and Belloq's enmity when he (a friend till then) betrayed Indy and stole a crystal skull they had found in Honduras, leaving Indy to be arrested by the local authorities (and explaining in turn the Noodle Incident mentioned in Doom). In Skull, the crystal skull is the Mcguffin, and Indy is betrayed by an old friend (Mac) and left to be arrested by the US Army in the Nevada desert.
Tribute to Fido: In Real Life as in-story, Indy is named after George Lucas's dog Indiana. In Temple of Doom, Willie was named after Steven Spielberg's dog, and Short Round was named after the dog of another crew member.
Had Sean Connery declined to appear in The Last Crusade, Gregory Peck was Spielberg's second choice to star as Henry Sr.
Tom Selleck was Spielberg's original pick as Indy, but Selleck was unable to get out of his contract to Magnum, P.I.., thus paving the way for Harrison Ford. Take a look at High Road To China (1983) to get an idea of what Selleck might have been like. We dodged a bullet there. Not to mention Ford's acting career might have ended with Star Wars just like most of his costars if George Lucas hadn't gotten him a second iconic role.
The DVD features include a screen test of Selleck, where he certainly doesn't display the charming badassery Ford brought to the role.
There were loads of unfilmed scripts written for Young Indy episodes before the series was canceled. One involved Indy meeting a young Rene Belloq and unearthing a crystal skull in South America, an idea Lucas reused (obviously) for the MacGuffin of Crystal Skull.
If The Other Wiki is to be believed about the production history of the fourth movie, we could've gotten it some fifteen years earlier with a very different plot if Lucas had not insisted on it involving extraterrestrials.
Also, at one point during the development of Raiders of the Lost Ark, Indiana Jones was originally envisioned to have a relationship with Marion when she was a small girl, and the idea was pitched by Lucas. It's probably for the best that they didn't go through with it, as it being kept would have led to implications that Jones was a pedophile.
The opening of the Ark and Nazi face-melting scene was originally much longer, which many felt was lacking in power. Everyone credits Lucas for personally re-editing the scene to be much snappier and memorable, so much that audiences knew they had to go back to see it again.
John Hurt's character in Skull was originally meant to be (an aged, slightly off kilter) Henry Jones Sr., but Hurt himself didn't like the idea of "stealing" Sean Connery's character, and he was re-written as Oxley. Of note is that virtually nothing was changed, they just name swapped him.
You Look Familiar: Every foe Indy fights that is larger than usual, except for Dovchenko in Skull, was played by the late British wrestler and stuntman Pat Roach. That makes the "giant sherpa" and the second German mechanic in Raiders, the Thuggee overseer in Doom and a German World War One pilot in a deleted scene of Crusade. You may know him also as General Kael, The Dragon from another Lucasfilm production, Willow.
Ronald Lacey, who played Toht in Raiders, appears as Heinrich Himmler during the Berlin book-burning in Last Crusade.
Sean Patrick Flannery, teenage Indy in the TV series, cameos as a patient in a mental asylum in Skull.
Paul Freeman, who played Belloq in Raiders, plays one of Indy's allies in the TV series, Great White Hunter Frederick Selous.
Vic Tablian plays one of Indy's Peruvian guides in the prologue of Raiders and the monkey trainer in the Cairo scenes. He returns in the TV series as recurring villain Demetrios, and after Demetrios is killed even shows up as an Armenian (finally Tablian's actual ethnic background) agent working in World War One Istanbul.