When you "go bananas" you behave in a slightly crazy or silly fashion. The expression is considered slang and is therefore used only in informal contexts.
The children will go bananas when they see the cute little puppy.
Aparna went bananas when she was introduced to Brad Pitt
When you find yourself in the midst of an argument on a subject that you have no knowledge of and an obvious polarization between the preferences, you can always pick the side of the venerable banana. It will get you nowhere, but at least you can say you participated.
Taken from the Simpsons episode in which Bart and Nelson race an orange and a grapefruit to the end of the schoolbus. Ralph Wiggum decides to join the race and puts a banana in the aisle and yells "Go banana!"
Punk 1: Hardcore and pop punk all teh way!
Punk 2: NO! DEATHCORE FTW
Punk 3: You're all stoopid. Rapcore is bomb.
Me: Go banana!