Pioneer 4 launched 1959

With pressure mounting for the U.S. to keep up with the Soviets, Pioneer 4, lunar probe, was launched March 3, 1959.   Luna 1, the first Soviet probe to successfully pass by the moon, had been launched in January 1959.  Pioneer 4 was the first U.S. probe to escape Earth's gravity.  It passed within 58,983 km of the lunar surface, but it did not come close enough to trigger its photelectric sensor, which should have been activated by the moon's light.

It did send back radiation data for about 82.5 hours before contact was lost March 6.  It remains in a heliocentric orbit.  Pioneer 4 was the only successful launch by the U.S. in twelve attempts between 1959 - 1963.  In 1964, Ranger 7 would finally surpass Pioneer 4's success by accomplishing all of its mission objectives.

Luna 1, first Soviet lunar probe, launched 1959

Luna 1, launched January 2, 1959, was the first probe to leave Earth's gravity and travel to our nearest neighbor, the moon.  Initially, it was intended to impact the lunar surface but due to an incorrectly timed upper stage burn during launch, it missed the moon by almost 6000 km (3725 mi) two days later. 

It still managed to collect some vital information. 

It is now in a heliocentric orbit between Earth and Mars.

Luna 1, first man-made object to reach the Moon, 1959

Luna 1, launched January 2, 1959 from the Soviet Union, made its closest approach to the Moon on January 4.  It was the first flyby of the moon by a man-made object, although it was meant to crash into the moon.  It missed the moon by about 3700 miles and remains in a heliocentric orbit between Earth and Mars.

It still managed to send back data on Earth’s outer Van Allen radiation belt and determined the Moon to have no discernable magnetic field.  Its flyby of the moon came one year to the day Sputnik 1 entered Earth’s atmosphere and disintegrated.