Moon landing: USA, Russia (USSR),
China
Spacewalk: USA, Russia (USSR),
China
Satellite Navigation system in operation: GPS (USA), GLONASS (Russia), Beidou (
China)
Asteroid landing: ESA, Japan
Mars mission - orbiting success: USA, Russia (USSR), India
Space rendezvous and docking of 2 or more spacecraft: ISS,
China
Living in space: USA, USSR (Russia), ISS,
China
Successful returning to / landing on Earth from space: USA, Russia,
China
Space telescope: USA
The furthest space objects flying in deep space: USA
USA is still by far the most successful in terms of space exploration.