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
by Kuri88 September 29, 2007
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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 3: You're all stoopid. Rapcore is bomb.
Me: Go banana!
by Yegs February 25, 2010
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'Go Go Bananas' is a ferocious war cry hollered by noble warriors when running off to tackle a problem in a courageous and sometimes suicidal head-on manner.

It's best said in a badly faked American accent for extra hilarity.
Private: "Seargent, the tangos are multiplying and out numbering us 100 to 1, we need to act fast!"

Seargent: "We'll hit them with a head on charge, and tickle their bottoms!"

Private: "Thats suicide, you'll kill us all!"

Seargent: "GO GO BANANAS!"

..many bottoms were tickled that day, lest we forget...
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