WALL-E ( Waste Allocation Load Lifter – Earth-Class) is your classic garbage collector left on Earth to clean up after the humans have left to seek refuge in space. He is alone except for his cockroach friend Hal yet he continues to do his job and even uncovers a seedling. He is lonely and is desperate for contact.
EVE (Extraterrestrial Vegetation Evaluator) is from the human spaceship and is a high class robot that only has her job on her mind. She is sent to Earth to look for life and instead find WALL-E. At first she pushes WALL-E away but soon learns to love him.
There relationship is a bit of an uphill battle as EVE goes into sleep mode to await transport back to the human spaceship, WALL-E hitches a ride on the outside of a rocket, cleaning machines want to throw WALL-E out with the trash, and both are attacked by a spaceship determined not to return to Earth.
In the end through commitment to each other they bring humans back to earth. Through their actions they showed the humans that human (and robot) interaction are worth fighting for.
To me that is a classic Disney romance.