Of course, once they had settled on land and found perfectly drinkable water there, they didn't really need beer... which didn't stop them from fighting over the beer that remained, and sending the first ship back to England with an order for plenty more.
The World-Changing Consequences:
Plymouth Colony became the oldest permanent English settlement in America, and their search for ideological freedom remained an important theme all through the history of the United States.
As did their obsession with beer.
The Pilgrims are responsible for much of American folklore, starting with Thanksgiving. Speaking of which, if the Pilgrims had run out of beer anywhere besides Plymouth, there's a good chance they would have been screwed. The Native Americans they happened to befriend (Pilgrim for "stealing their corn") at Plymouth had a guy who spoke English, and were friendly enough to teach them how to survive in that area. Without that stroke of good luck, the Colony doesn't survive that first winter.
In other words, if the murmurs of "keg's tapped" and "this party's lame" had started a few miles down the coast, none of us would be here right now.