The motif of the three wishes is an old inheritance from oral tradition, shared by European and Middle Eastern folklore. The Danish folklorist Axel Olrik (1864-1917) described what he called the "Rule of Three" as a dominate component of European folklore, so this single aspect of the popular image of Aladdin cannot be credited to the 1992 film.

Similarly, the story of Aladdin (which includes the three wishes), though a later addition to A Thousand and One nights was nevertheless a popular part of that collection as soon as Sir Richard Burton published his translation in 1885. Its subsequent appearance in British folklorist, Andrew Lang's first "fairy book," The Blue Fairy Book (1889) added to the popularity of the story.

Various films beginning in 1926 extended the reach of the story. The 1992 film is imaginative and created its own following in a new generation, but I don't think we can credit it with having a particularly prominent role in bringing to the fore the idea of a genie, the motif of the three wishes, or any other aspect of the Tale of Aladdin.