There are a lot of different reactions depending on the year you're referring to and the location/demographics etc. In general as the Americans advanced into the country they were reasonably well received by a population exhausted by war, mistreated by retreating German soldiers and moderately terrified that the Soviets would get to them first. The appearance of well fed Americans, with clean new uniforms and food and cigarettes to spare left a major impression as well. This laid the seeds that the American way may be superior to the German one.

The initial years of the occupation were very rough on the German population as even the population in the American zone saw a 65% reduction in their daily caloric intake and other metrics like infant mortality rose significantly. Despite this, there was not a significant backlash towards the Americans, as their occupation was certainly less punitive than the Soviets and even the French. After the establishment of West Germany the Americans were the primary military force in West Germany and here is where the reactions most sharply diverged. Young people embraced the US most openly and adopted many aspects of American culture, the traditional lower classes also looked favorably upon the US as they provided employment which paid far better than they could earn otherwise and allowed them to lead a lifestyle previously out of reach and more in keeping with that of the traditional middle to upper classes. These classes looked less favorably on the occupation and felt the US was subverting traditional values. The CDU under Adenauer tapped into this and attempted to take a number of measures aimed at protecting the cultural integrity of the country and saving the youth. These included charging women who dated Americans with prostitution, closing down bars where Americans, particularly black GIs, drank and trying to limit access to some of the major towns. These efforts largely failed as American commanders pushed back and residents of the town complained about the unjust imprisonment of their relatives and substantial loss of revenue. Attitudes towards the US did not take a significantly negative turn until the mid-1960s when American involvement in Vietnam became an increasingly touchy issue and student groups mobilized in protests and even some terrorist action against US Soldiers. This led to a pull back from communities and less open relationship.

Postwar by Tony Judt covers this in broad swaths and GIs and Frauleins: The German-American Encounter in the 1950s West Germany by Maria Hohn offers an in-depth and interesting look.

Edit: Corrected my math to 65% not 75% and changed the party to CDU rather than CDP, thanks /u/vraid and /u/ChuckCarmichael

I could type pages over pages if "My Grandparents said.." would be permitted, but instead Im going to stick to a single source that you can observe for yourself to see how the germans saw the US.

The source Im talking about is the JFKs 1963 visit to Berlin. http://www.youtube.com/watch?v=oDP_98MCues Of course the Americans were occupying the country, but elections took place as soon as you could really expect them, the industry and cities where beeing rebuild and an era of growth began ("Wirtschaftswunder").

The Americans were the ons supporting and maintaining this new very positive status quo and just as importantly keeping Germany free against the threat of communism.

Edit: Look at cubshounds comment for the best answer so far. http://www.reddit.com/r/AskHistorians/comments/1uwp04/how_did_german_citizens_view_americans_during_the/cemo9ba

While not specific to the question of German views of Americans, They Thought They Were Free: The Germans, 1933-45 by Milton Mayer was written during the post-war period by an American living in Germany, and touches on how Germans viewed America in several instances.

There were three Western occupation zones with 60% of the population and less than 40% of the food production - so while the German population was facing deNazification and other difficulties of occupation - this was countered by the West giving relief from Soviet pressure, and feeding the people so morale was relatively good.

here is a decent essay on the topic: http://histclo.com/essay/war/ww2/after/ger/occ/occ-west.html

Edit to add: The Wikipedia article on deNazification has a decent list for further reading - the article itself discusses some of the difficulties http://en.wikipedia.org/wiki/Denazification#Further_reading

While certainly not representative of all germany at the time, A German Community Under American Occupation: Marburg, 1945-52, by John Gimbel talks about how the people of Marburg viewed american occupation. It certainly doesn't give the whole view of the situation, but talks about how the Germans felt during the occupation, though I can't speak for the merit of hist writing as a whole. Right now I'm having trouble finding good secondary sources or any primary sources that would explain this subject better or more to the point that aren't behind a paywall. There seems to be a lot of anti-american sentiment early on in the occupation (Americans were directly responsible for a policy called "Denazifacation" before they handed that off to German government in 1946, which resulted in the dismantling of nazi power-structure and local government institutions) but to what extent I don't know.