Ice, Ice, Baby
Woe to the American who wants an ice-cold beverage while traversing Europe. Ask for ice in your soda and you might be treated to one or two cubes, a far cry from the filled cups much of Americans are accustomed to. As with any cultural preference, there's probably not one simple reason why Europeans and Americans vary so widely on the topic of ice, but it's likely that the 20th century modernization of America played a role. While U.S. households became rapidly equipped with refrigerator/freezers that easily dispensed ice, Europe lagged behind. Instead, Europeans were shipped ice from North America and asked to pay laughably high prices for something they weren't even accustomed to using. As a result, ice never really took off there, and is sometimes even seen as a drink diluter [sources: Cutolo, Bramen].
The American fascination with ice could also be related to an early belief that it prevented illness-causing bacteria. In 1851 a doctor named John Gorrie obtained a patent for an ice machine because he believed that cooled air (accomplished by hanging ice from the ceiling) could make exam rooms less infectious. Then in the 1950s, Kemmons Wilson, who founded the Holiday Inn chain, became the first to install ice machines in his motels, thus ensuring free availability of the product from coast to coast [source: Julavits].
But the most likely reason Americans love ice might simply be because many areas of the country get really really hot for a significant part of the year (unlike say, England, France or Scotland). Thus, a literally ice-cold beverage brings much-needed relief.