The US used to fly directly over USSR airspace quite often in the 1950s, look up RB-50 and RB-47 on Google, some interesting history. Most of these breaches were confined to the high arctic and the eastern parts of Siberia; they generally stayed away from sensitive areas. Once the U-2 came online around 1953 they switched most missions to that. Overflights were permanently suspended by Eisenhower after the famous U-2 shootdown.

After that the US ramped up its satellite surveillance capabilities but still flew numerous missions right up to the 12-mile sovereign territory limit. SR-71s were often used for this well up to the late 1980s to get the USSR to switch on its early warning systems and radio nets so data could be gathered. The US did conduct overflights of proxy Cold War countries such as Vietnam, North Korea, Cuba, and Nicaragua, but stayed out of Eastern Europe.

I am not aware of any Soviet overflights over the US, who had a far superior early warning network and a large Air Defense Command presence around its periphery. I remember around the 1980s there was a stray Tu-95 or Tu-142 overflight of Norfolk that led to some diplomatic protests.