Eternal Sunshine of the Spotless Mind (2004) on Netflix

This is the story of a guy, Joel, who discovers that his long-time girlfriend, Clementine, has undergone a psychiatrist's experimental procedure in which all of her memory of Joel is removed, after the couple has tried for years to get their relationship working fluidly. Frustrated by the idea of still being in love with a woman who doesn't remember their time together, Joel agrees to undergo the procedure as well, to erase his memories of Clementine. The film, which takes place mostly within Joel's mind, follows his memories of Clementine backwards in time as each recent memory is replaced, and the procedure then goes on to the previous one, which is likewise seen, and then erased. Once the process starts, however, Joel realizes he doesn't really want to forget Clementine, so he starts smuggling her away into parts of his memory where she doesn't belong which alters other things about his memories as well...