End of Days: Man with peculiar accent tries to prevent a pregnancy.
Equilibrium: A handsome man falls in love with his recently deceased coworker's girlfriend. His interactions with her and a lovable puppy inspire him to confront his boss and quit a job he never truly liked. Can be seen on the Lifetime Channel.
Alternatively, In a futuristic dystopia that has outlawed emotions, a former enforcer of the system must fight for freedom with laughably unrealistic gun-fighting skills.
Eraser: Man with peculiar accent helps people play Hide-and-Seek.
Eraserhead: A man encounters difficulties trying to raise his deformed child.
The Elephant Man: Circus performer quits job, lives in a hospital, befriends Hannibal Lecter and Mrs. Robinson.
Escape from New York: Police arrest badass criminal and order him to break into a very large prison under the threat of exploding his neck.
Escape from L.A.: The exact same thing as above, but from different camera angles. This time, after the criminal is done, he helps everyone save on their electrical bills.
E.T.: Some misfit suburban Emo kid gets high with his alien friend whom his mom doesn't think is real and might be Jesus.
Eternal Sunshine of the Spotless Mind: A man dreams about his ex-girlfriend before meeting her on Valentine's Day. They end up going on a date to a lake they used to visit, but they both become upset when she finds a tape of him complaining about her. The moral of the story? Brain damage will bring you closer together.
Or: Boy meets girl. They break up. Girl forgets boy, so boy expresses grudge by forgetting girl. Boy withdraws his consent to the memory wipe right in the middle of the memory wipe. Post-production lazily avoids putting the scenes in order.
Event Horizon: Members of a towing crew get on each others nerves after being sent to tow a missing vehicle. The vehicle's new owner goads them over their past mistakes, encourages them to perform do-it-yourself surgery on their faces, and wants them to relocate to a new home.
Everything Is Illuminated: Frodo goes to Ukraine in search of his grandfather's ex-girlfriend, finds an old lady in a house filled with boxes. A blind grandpa does the driving and a rock star (without his famous mustache) translates.
Everything You Ever Wanted To Know About Sex But Were Afraid To Ask: The Film of the Book of a sex guide.
The Evil Dead (1981): Camping trip takes a turn for the worse when the hero's car conks out. The fertility rites of nature are explored in detail. Reading books is bad for your complexion.
Evil Dead 2: Man has another bad camping trip (or perhaps the same one), then beats himself up about an upcoming surgery. Furniture laughs at him.