Both the Korean and Vietnam Wars enabled the Soviets to gain examples of American aircraft. In 1951 an F-86 ditched into coastal mudflats and the Americans were unable to destroy it. The F-86 was hurriedly packed off to the USSR (according to some engineers, they didn't even bother washing off the mud) and its components were dissected by the Soviets.

North Vietnam's successful invasion of the South allowed the Soviets to gain access to the flyable models of the F-5 and OA-37. Soviet pilots were very impressed with the former. Here's video of the F-5 being tested by the Soviets. One of the F-5Es is currently in a museum in Poland. Even more enigmatic are several photos from Zhukovsky showing what appears to be an F-4 and Mirage fighter. The best consensus is that like the F-86, the airframes were non-flyable models cobbled together from either Vietnam or the Middle Eastern sources. During the 1980s there were also persistent rumors that the Soviets had gotten their hands on both an F-14 and/or an AIM-54 from the Iranians during the 1980s, but Yefim Gordon's tome on US aircraft in the USSR doubts this.

One of the best resources for information on NATO equipment was a judicious analysis of open-source information in Western trade journals and the defense press. A declassified CIA memo on Soviet knowledge of American stealth programs concluded that Soviet intelligence used the press to gain a general idea of the contours and details of the various stealth programs.

Source

Gordon, Yefim. US Aircraft in the Soviet Union and Russia. Hinckley: Midland, 2

Just a reminder to anyone answering: confine answers to events prior to 1996 per the sub's 20 year rule. Thanks!