Yes, there were extensive rapes by American soldiers during the Second World War.
During the Second World War American GIs in Europe raped around 14,000 civilian women, in England, France and Germany. There were around 3,500 rapes by American servicemen in France between June 1944 and the end of the war ... some Allied troops were punished for sexual violence, including the execution of 70 American soldiers.
- Brown, Jennifer M., and Sandra L. Walklate, eds. Handbook on Sexual Violence. Routledge, 2011.
Keep in mind that while high in absolute terms, it did take place during a brutal war involving tens of millions of soldiers. Though rape by American soldiers was not "isolated cases", it certainly was no where near the same scale as the Red Army's atrocities either.
Authorities did try to deal with the problem, especially in France. Raping civilians of allies being less tolerated. Notably however, the Army scapegoated black servicemen for reported crimes:
[T]he public hangings scapegoated black soldiers for the crime of rape in order to save the reputation of the US Army ... [Reports] demonstrate a growing inclination among military authorities to make rape a "negro" not an "American" problem.
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152 American soldiers had been tried for rape; of these 139 were "colored."
- Roberts, Mary Louise. What Soldiers Do: Sex and the American GI in World War II France. University of Chicago Press, 2013.
This was not because black GIs were more likely to commit rape (which isn't to say it wasn't more likely, mind you - just that they were disproportionally punished for it). Black soldiers were at risk of being scapegoated on a personal basis for the crimes of their white counterparts.
White soldiers could rape a French white woman with impunity if an African American was in the vicinity and could be plausibly blamed. In several cases, black soldiers were picked up in the vicinity of the rape, and charged on those grounds alone, without any physical evidence or witness identification to prove their presence at the crime.
- Roberts, Mary Louise. What Soldiers Do: Sex and the American GI in World War II France. University of Chicago Press, 2013.
John Willoughby's "distressing account of an undisciplined and marauding mob" (according to a review) discuss this in the immediate post war years, citing Morris MacGregor's Integration of the Armed Forces.
Ulysses Grant Lee maintains that the VD rate of black American troops was often lower than that of the black civilian population in the South. Given this historical condition, it is not surprising that African American venereal disease rates were higher than those for white soldiers ... It is important to note that there is no compelling evidence that black’s sexual activity was significantly different than whites’.
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"[An explanation was] commanders' power to define serious offenses." Officers were more likely to interpret black contacts with the female population hostilely, while forgiving white soldiers for their "youthful indiscretions" ... White soldiers were more likely to avoid rape charges even when they were guilty of the crime.
- Willoughby, John. Remaking the Conquering Heroes: The Social and Geopolitical Impact of the Post-War American Occupation of Germany. Macmillan, 2001.
In addition to war time rapes, there were also quite a large number of rapes during the occupation. The situation was relatively better for Japan (after an initial frenzy): the Japanese government organised "comfort women" to pleasure American soldiers on a large scale.
Many GIs held the Okinawans in open contempt ... Rape became so common place in the wake of battle that the Army decreed the death panelty for offenders in an attempt to curb its incidence.
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When US paratroopers landed in Sapporo, an orgy of looting, sexual violence and druken brawling ensued. Gang rapes and other sex atrocities were no infrequent ... In the first 10 days of occupation, there were 1,336 reported rapes by US soldiers in Kanagawa Prefecture alone.
- Takemae, Eiji. Allied Occupation of Japan. Bloomsbury Publishing, 2003.