At the end of this segment, Bender bursts through the screen saying, "T-t-t-that's all you get, ya jerks!". This is a reference to the end of most Looney Tunes episodes where Porky Pig bursts out of a drum saying, "T-t-t-that's all, folks!"
The second act is a parody of many video games.
In the second segment, when the professor determines the meaning of everything, it seems to parody art games like "Every Day the Same Dream" and "One Chance".
After the professor has solved all the questions of the universe, there are many references to various video games: Space Invaders, Boulder Dash with 'Digger', Donkey Kong, Tapper, and Dig Dug, and the clouds and pipe from Super Mario Bros. 2 (Japan only version).
The third act can be a reference to Japanese animation shows.
Amy's hairstyle in the third segment seems to be a parody of Sailor Moon.
In the third segment, Some of the music is actually from real anime shows, esp. Voltron and Macross.
Bender transform into to a bigger and more powerful robot, which can be a reference to the movies Transformers.