Yes, female pilots served in some nations. Since you asked for nations other than Russia, I will leave the Soviet Union out.

The British Royal Airforce had the Air Transport Auxiliary (ATA), in which men and women served. The men were veterans of WWI that were too old to serve in WWII, or had health issues that made them unfit for regular military service. With a wink, they used to say that ATA would mean "Ancient and Tattered Airmen". Of more than 1,300 pilots, only 168 were female. They were experienced in civil aviation and recruited in late 1939. They were only allowed to fly non-combat planes. This changed in July 1941, when the Royal Airforce was in urgent need of male pilots for an upcoming offensive, after it lost many able pilots in the Battle of Britain. In most cases, ATA pilots had no experience flying the planes they had to convey, and they were only given a handbook showing the basic instruments and 20 minutes of time before flight. Besides, Great Britain had no air superiority in the beginning of WWII, and during ferry flights, the planes were unarmed or no ammunition was provided, so there always was a risk of being shot down by a German Bf-109. When the war went on, more inexperienced pilots were recruited, and a training programme was established, to make them "experts" in a category of planes (like planes with one engine, planes with 2 engines, flying boats etc.)

Many pilots in the ATA were foreigners, they either fled from Nazi occupation (there were some from Poland, for example, as well as in the Royal Air Force), or were volunteers from other countries. One of them was Jaqueline Cochrane (United States), who returned home after the United States joined the Allies, and she founded the Women Airforce Service Pilots (WASP). It consisted of 1074 female pilots, their mission was flight-testing, ferry flights, and towing targets in weapon training for combat pilots.

Germany had no particular unit or programme for female pilots. This would have also interfered with the role of women in Nazi ideology. Some of them, however, who were famous civilian pilots before the war, were employed by either the Luftwaffe (in the Überführungsgeschwader, "ferry squadrons") or the plane manufacturers. Their role was the same as for female pilots in UK and the United States: flight-test, ferry flights, towing targets. The most known are Beate Uhse and Hanna Reitsch, who test-piloted the Junkers Ju-87 Stuka and the Dornier Do-17 bomber. She also suggested a Kamikaze-like programme to Hitler, using manned V-1.