Cocktails/mixed drinks had been around since the 19th century, but did experience an uptick in popularity with prohibition for several reasons, one of which was that there was a lot of bad (or even dangerous) bootleg liquor going around, and mixers helped mask the taste. They were also apparently valued since the lighter taste made them easy to finish quickly if police came knocking.

After prohibition, alcohol interests looked to cocktails as a way of keeping it from being reintroduced, both by giving drinking a more stylish, high-society image and by marketing them towards women, who were traditionally the largest group of abstainers.

Other effects included shifts in types of alcohol. Spirits became more popular during prohibition for their higher alcohol content by volume (though I'm not sure if that shift endured after Prohibition's end). Much of the fledgling wine industry in the US was strangled and took time to recover.

Americans also drank a lot less afterwards, with consumption immediately after prohibition at 30% at what it was prior to it. It recovered to 60-70% pretty quickly, but didn't fully recover until the 60's or 70's.

Where drinking occured also shifted a lot. Pre-prohibition saloons tended to be rather rough places, but during prohibition people had to drink in their homes or in speakeasies, and that endured after Prohibition, with most US drinking occurring at home or in private parties.

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1470475/

On the same note, is it true that spirits were a lot stronger during prohibition so that getting drunk required less booze?