Snopes debunked it.
In short: Sales of Coke was waning, and Pepsi was winning. So Coca Cola changed the recipe to be more like Pepsi and made a big campaign about the new recipe. This got people upset, as they felt it violated something that was an integral part of being American. People therefore demanded the old Coke back, which they got after a couple of months. The whole debacle made people who felt American switch from Pepsi to Coke, and boosted Coke sales.
The conspiracy is that all of this was intentional from Coca Colas side, which of course is completely ridiculous.
Additional reference: http://www.bbc.co.uk/programmes/b010tbnd