First contact was the ambiguous term used to describe a planet's first official contact with "alien" life.
Human first contact
The human race had come into contact with many alien races before first contact, (TV: The Invasion, The Tenth Planet, AUDIO: Storm Warning et al.) but most invasions were covered up by the government (PROSE: Who Killed Kennedy, The Forgotten Son) or just assumed by the public to be hoaxes. (AUDIO: The Kingmaker)
In the late 19th century, Jack Harkness told a Blowfish in Cardiff that the Earth was a century away from official first contact. (TV: Fragments)
First contact policy was decided by the United Nations Security Council in 1968 (TV: The Sound of Drums) but was inherently outdated, as around half a dozen nations were covering up the existence of aliens from each other. It became deliberate policy under Secretary General Kurt Waldheim to cover up all alien contacts to prevent a destabilisation of the world order. (PROSE: The Dying Days)
Some accounts indicated that the general public accepted extraterrestrial life as fact following incidents such as the Gantacian invasion of 1992 (COMIC: Invaders from Gantac!, The Mark of Mandragora) and the Availlon fiasco of 1997. (TV: Battlefield, COMIC: The Mark of Mandragora)
In 2006, the Ninth Doctor witnessed an alien ship crash into Big Ben. He believed this to be the first contact for humans on a large and newsworthy scale. Though the porcine pilot of the ship wasn't a true alien, the spaceship crash and the genetic engineering to create the pilot was caused by a Raxacoricofallapatorian family, the Slitheen. (TV: Aliens of London) The entire event was considered a hoax by at least the press. (TV: World War Three)
On Christmas Day 2006, a live broadcast of a Sycorax was broadcast on the news. It was believed to be a hoax, but when the Sycorax ship hovered over London, with Harriet Jones later speaking to them on behalf of humanity, their existence was confirmed, (TV: The Christmas Invasion) if still denied by some as having actually happened. (TV: The Runaway Bride, Everything Changes)
In 2008, the Saxon Master, under his alias Harold Saxon which he used to become the British Prime Minister, introduced the Toclafane as a race of peaceful aliens who wished for friendship and diplomatic relations with the people of Earth. When the first contact was taken over by UNIT and the American President Arthur Coleman Winters, the Master and the Toclafane revealed their true colours and began an invasion of Earth. Their year-long rule was negated by the Tenth Doctor. (TV: The Sound of Drums)
Having previously negotiated in secret, their interests represented by the Torchwood Institute, with an alien race nicknamed the 456 in 1965, the British government was forced to reveal this to UNIT and the international community in 2009 when the 456 returned and demanded 10% of the Earth's children. (TV: Day Three) The 456 were thwarted by Jack Harkness, the leader of Torchwood Three. (TV: Day Five)
Humanity's first recorded official peaceful first contact with aliens was the Arcturan Treaty of 2085. Some historians counted this as Real First Contact as government secrecy made it nigh-impossible to work out the actual first contact. (PROSE: The Dying Days)
Other references
Gwen Cooper colloquially referred to her kiss with the sex gas-possessed Carys as "first contact with aliens", saying that it wasn't quite what she expected. (TV: Day One)