The Twilight Zone
Early in the episode, Fry and Bender were watching "The Scary Door", which is similar in style to The Twilight Zone. The opening is similar. Also, the episode itself was a reference to an old TWZ episode, Time Enough at Last, about the last man on earth using all the time in the world to read...at least until he breaks his glasses. The only difference is that, in this parody, after the man breaks his glasses, he keeps going for the books...until all of his body parts fall off.