We all know that Indiana Jones is such a huge icon in the realm of pop culture, then it was no doubt that Indiana Jones would end up in the world of Big Bang Theory.
The first reference to Indiana Jones was in the season 3 episode The Precious Fragmentation, where Sheldon, Leonard, Raj and Howard follow a guy "who looks like Adam West" to a garage sale, where they buy a box of stuff for $60. When they look through the box, Leonard pulls out an original Temple of Doom connect-the-dots book
It wouldn't be the last time that Indiana Jones would have been mentioned, in fact, the first episode dedication to Indy was in season 4. In an episode called "The 21-second Excitation", in which Sheldon, Leonard, Raj and Howard have finished watching Raiders and they find out that their local theatre is playing a special edition of Raiders, with an extra 21 seconds of footage, explaining how Indy stowed away onboard the U-Boat. The guys spend hours and hours waiting in line to go see the movie, but however, Wil Wheaton, Sheldon's arch nemesis, beats him into the theatre, Sheldon hatches an ingenious plan to break into the unattended projectionists booth and then steal the film reel. As he's running off with the reels under his arms, the final scene echoes Raiders in that Sheldon screams "why is there never a plane when you need one?" referring to Indy's escape from the Chachapoyan Warriors to Jock's plane.
The most recent episode of Big Bang Theory to feature Indiana Jones was the season 7 episode "The Raiders Minimization", in which Sheldon shows Amy Raiders for the very first time. She upsets Sheldon by stating that Indy wasn't needed in Raiders and therefore, if he wasn't in the movie, things would have panned out the exact same way. This disheartens Sheldon, as it's one of his favourite movies and he claims to have seen it over 35 times, except the parts with the snakes and melting faces, which he refuses to see after dark.
During the course of the episode, Sheldon, Leonard, Raj and Howard keep trying to find ways of proving Amy wrong about Indy being extraneous to the plot, but they keep finding out that she is right. Even Howard, who points out that if Indy wasn't there, the Ark wouldn't have ended up in the warehouse, Leonard points out that Indy was supposed to take it to the Museum, but he failed in that.
However, Indy was actually needed in one point, which Amy missed. The Nazis needed Indy to pinpoint the location of the headpiece, which they didn't know until they followed Indy to Nepal and with Abner dead and his journal in Indy's hands, the Nazis had no way of knowing where the headpiece was.