u/Romboteryx

Young Frankenstein: Mel Brooks‘ parody cemented the idea that Dr. Frankenstein has a hunchbacked assistant named Igor/Ygor, which has become an expected staple in subsequent adaptations of the book. In the original story, Frankenstein has no assistant. A hunchbacked assistant is introduced in the first movie from 1931, but there he is named Fritz. Son of Frankenstein has a character named Ygor, but he isn‘t an assistant but an undead ghoul and the villain of the movie. Young Frankenstein is the first to have an actual assistant character named Ygor.

Spaceballs: This is technically just speculation, but there is no way at least someone working on Rogue One didn‘t think of Druidia when coming up with the planetary shield of Scarif.

Hardware Wars: This is George Lucas‘ favourite Star Wars parody and Rian Johnson included a homage to it in The Last Jedi.

Austin Powers: As revealed by interviews with Daniel Craig, the newer James Bond movies had to seriously tone down the more fantastical and horndog elements, because Austin Powers had so devastatingly lampooned the older movies that nobody could take them seriously anymore. Alotta Fagina lowkey does sound like a more believable name than Pussy Galore.

Monkey Island: The games took a lot of their aesthetics from the Pirates of the Caribbean theme park ride at Disneyland. The first POTC movie in turn took inspiration from the script of the planned but cancelled Monkey Island movie (allegedly).

Shrek: Similarly to the Austin Powers example, Shrek parodied so many fairytale tropes popularized by Disney movies that its massive success meant general audiences could no longer take them seriously. It arguably killed the Disney Renaissance, indirectly leading to the end of Michael Eisner (caricatured in the movie through Lord Farquaad) as CEO of the company. The effects of this are still felt decades later when Disney went back to fairytale stories, with films like Frozen being self-aware and poking fun at their own clichés.

Galaxyquest: On top of being beloved by many veteran Star Trek actors, the characters from this movie actually ended up in the official Star Trek videogame Star Trek Fleet Command