This thread is rather old, but sure!
1944: Nazi rocket scientist Klaus Riedel survived the car accident that would've killed him in OTL.
1945: Anthony Marchione was shot down by part of the Imperial Japanese air force, causing General Mcarthur to interpret this as an act of non-surrender. Small skirmishes between US and Japanese forces ensued but it was quickly brought to a resolution fortunately. At the same time rocket scientists Rudolf Nebel and Klaus Riedel are recruited by the US.
October 4, 1957: USSR launched Sputnik 1 into space, which is the first artificial satellite.
November 3, 1957: Sputnik 2 is launched, carrying Laika the first dog in orbit.
December 6, 1957: The US launched its first satellite into space, Vanguard I.
January 31, 1958: USA sent up another satellite Explorer I into space.
March 5, 1958: NASA's Explorer II is launched into orbit.
April 27, 1958: Sputnik 3 launched by USSR.
December 6, 1958: Pioneer 3 is launched that will became the first object to impact the Moon.
January 2, 1959: SU takes one step further by sending Luna 1 into the cislunar space and beyond.
January 20, 1961: Inauguration of President Kennedy.
January 31, 1961: NASA sent up Ham the Chimp into space.
April 12, 1961: Cosmonaut Yuri Gagarin became the first man in space and in orbit, however his mission is a partial failure since Vostok's retrorockets failed before intended reentry causing him to enter the code to unlock the controls and attempt to control his spacecraft to no avail. Fortunately he safely landed inside the United States due to natural orbital decay in lower orbits few days later.
May 5, 1961: NASA's Alan Shepard is the first American in space with a 15 minute suborbital flight, and with a recoverable booster.
May 25, 1961: US President Kennedy delivers his speech to put a man on the Moon in the Congress. Afterwards Khrushchev orders Korolev to do the same thing.
July 21, 1961: Mercury Redstone 4 carrying Gus Grissom commences with the usage of the booster recovered from Shepard's flight.
February 20, 1962: John Glenn became the first American to orbit the Earth.
July 22, 1962: Mariner 1 is launched, and would become the first probe to fly by a planet (Venus) later.
November 1, 1962: Yevgeni Andreyev and Pyotr Dolgov survived their space dive. Soviet probe Mars 1 is successfully sent to the direction of Mars.
June 16, 1963: Valentina Tereshkova is the first woman in space.
June 19, 1963: Mars 1 closest approach at 193,000 km from Mars. It also sent back first close-up images of the red planet.
March 18, 1965: Alexei Leonov is the first person to do a extravehicular spacewalk.
November 2, 1965: Voskhod 3 lifts off into space and flew into the vicinity of the Van Allen Belt.
February 3, 1966: Luna 9 is the first object to soft land on the moon.
March 15, 1966: Irina Solovyova is the first woman to spacewalk in the Voskhod 4 mission.
January 27, 1967: Apollo 1 does not have a disaster in TTL.
April 26, 1967: Soyuz 1 performed a hard landing onto the ground. Vladimir Komarov survived but is permanently left disabled.
Mid-1968: Apollo 7 made a circumlunar flight around the Moon, but not into orbit.
November 15, 1968: USSR launched Alexey Leonov and Valery Bykovsky in a Soyuz 7K-L1 spacecraft to do a lap around the Moon like Apollo 7.
December 24, 1968: Apollo 8 became the first manned mission to orbit the Moon.
February 19, 1969: Lunokhod 1 rover is sent to the Moon where it successfully lands, stunning the world.
May 17, 1969: Yuri Gagarin and Viktor Gorbatko became the first Soviet cosmonauts to orbit the Moon in a Soyuz 7K-LOK spacecraft.
July 20, 1969: Apollo 11 landed on the Moon which is the first manned mission to do so.
November 4, 1969: USSR followed suit by sending Alexei Leonov to land on the Moon.
March 1970: In tandem with the lunar mission, NASA launched the world's first space station "Olympus" based on
LM lab design. There would be two missions to dock on it and conduct experiments.
December 15, 1970: Venera 7 soft lands on Venus.
April 12, 1971: Launch of Salyut 1 the second space station.
April 22, 1971: Soyuz 10 launched which will become the first manned mission to enter the Salyut 1 station.
June 12, 1971: Soviet Russia's Irina Solovyova is the first woman to walk on the Moon.
March 2, 1972: Pioneer 10 is launched to Jupiter.
April 6, 1973: Pioneer 11 is launched to Jupiter and Saturn.
October 6 - 25, 1973: Yom Kippur War.
Circa 1974: Mariner 10 is the first to reach Mercury while Pioneer H is launched as an out-of-the ecliptic mission.
July 15, 1975: Apollo Soyuz test project is launched into space.
Early July 1976: The final Apollo 22 mission is the first working base on another celestial body with the deployment of a
lunar shelter, dealing a final blow to the Soviets in the race for space supremacy.
July 20, 1976: NASA's Viking 1 lands on Mars and successfully performed its mission.
September 5, 1977: NASA launched Voyager 1 to the outer planets and beyond.
April 12, 1981: Space Shuttle Columbia makes its maiden flight.
March 9, 1989: Start of a series of revolutions in the Eastern Bloc.
November 9, 1989: Fall of the Berlin Wall.
December 26, 1991: End of the Cold War as the USSR vanish from existence.
November 16, 1996: Russia's Mars 96 is launched to Mars.
October 7, 2001: U.S. invaded Afghanistan.
March 20, 2003: USA invades Saddamist Iraq.
January 19, 2006: NASA launches space probe New Horizons.
October 9, 2006: North Korea explode its first nuke.
September 10, 2008: The Large Hadron Collider is activated by CERN.
January 20, 2009: Barack Obama is inaugurated as POTUS.
December 18, 2010: Start of the Arab Spring.
November 9, 2011: Phobos Grunt is launched to Mars.
April 13, 2012: North Korea launched its first satellite into space.
July 14, 2015: New Horizons flew by Pluto.
January 20, 2017: Hillary Rodham Clinton is inaugurated as the President of the United States.