Of course, proof of absence is a very hard thing to achieve, but I'm going to argue that the US Army at least absolutely did not organize military brothels in Western Europe.
My main source is What Soldiers Do: Sex and the American GI in World War II France by Mary Louise Roberts. This book is somewhat unfavorably reviewed on Amazon by veterans who state that the book misrepresents the position of the Army (and of individual soldiers) at the time by suggesting that the Army actually enticed soldiers with promises of easy sexual relations. These veterans argue that the Army was actually discouraging them to have any sexual relations. Seeing that the main criticism leveled at the source is that it might paint the image of an Army to lenient on sexual mores, I think it safe to use it to establish my point.
According to Roberts, the US Army was very forceful in not condoning brothels in Western Europe as that would have in all likelihood seriously damaged the glorious image of virtuous fighters US soldiers had to project for the home population to remain in favor of the War. Besides, mass prostitution spreads venereal diseases and a well-organized army wants healthy soldiers, so that the official policy of the US Army was to warn against prostitution and to advise chastity.
It turns out that this health concern was not ill-founded, as 1) the use of the (then perfectly legal and institutionalized) French brothel system, 2) occasional prostitution and even 3) rapes all seem to have been quite massive in late 1944, early 1945 ; apparently especially in north-western France, with the expected health (and social) consequences. At least the first 2 were probably to be expected with the massive influx of relatively rich Allied soldiers meeting an impoverished French population who had suffered 4/5 years of occupation. This elicited official protestations from French officials, most notably the mayor of Le Havre, Pierre Voisin. He pleaded for the institution of an official military run brothel in the hope that this would help control 2) and 3), which, he described, was jeopardizing the already very fragile reconstruction of normal society in a city which had just been freed from a difficult occupation and had been heavily bombarded by the Allies. The Army adamantly refused.
Seeing that it refused a direct request from an official to do so, I thus think it very unlikely that the US Army ever organized any military brothel in Western Europe during WW2.
Not limited to Nazi-Germany and Imperial Japan the following belligerents are implicated in providing women for sex to military authorities, Indonesia, Hong Kong, Singapore, the Philippines, and Thailand. A series of searches revealed an informative article. A snippet of this credibly sourced article is provide below.
During the Second World War, approximately 3,500 Australian military nurses served in combat regions throughout the world. The vast majority were enlisted in the Australian Army Nursing Service (AANS), but after the Japanese advance and the fall of Hong Kong (December 1941) and Singapore (February 1942), a significant number of these nurses spent three-and-a-half years as POWs in Indonesia, Hong Kong, Japan and the Philippines.1 To date, considerable research has been undertaken on POW experiences in Hong Kong, Singapore, Thailand and Japan, albeit primarily focused on the testimonies of men and civilian women.2 This body of research utilises various methodologies, from Yuki Tanaka and Kei Ushimura’s efforts to reconcile Japanese war crimes with the corruption of the Bushido ethic and sexual violence in contemporary Japanese society, to Christina Twomey’s work on the imprisonment and repatriation of Dutch, Dutch–Eurasian and Australian civilian women and children. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3143890/