If we learn anything from WALL-E, it's that having a hard copy of a movie around— whether it be a DVD or WALL-E's format of choice, the VHS tape—is better than Netflix. In the world of WALL-E, there is no Netflix. There is no 'Net to have 'flix on, so all the movies in its database would be gone. WALL-E wouldn't even know they existed.
With a tape, though, WALL-E can watch it. He has one tape that he watches over and over, and that's Hello, Dolly! a 1969 film starring Roz Focker and Albert Einstein. This matchmaking musical mimics WALL-E's own journey, traveling to a new place (outer space as opposed to New York) and finding a match of his own.
This movie teaches WALL-E how to love. It's one thing to experience vicariously through a film, but WALL-E wants to feel it himself… which is why he follows EVE to infinity and beyond.