Alternate timelines
In an alternate timeline created by the Discordia, the Doctor had a passionate romantic relationship with River Song that began in his first incarnation, having married her by his fourth incarnation. In one of their outings, River convinced the Doctor to dress as Ramón Salamander for "fun". (AUDIO: Someone I Once Knew)
In an alternate version of the London Event, the Doctor was killed by Colonel Spencer Pemberton in the London Underground. (PROSE: Legacies)
Averted timelines
When the Cybermen allied with Rassilon to take over history, (COMIC: Supremacy of the Cybermen) they manipulated the encounter at the Moonbase so that the Doctor was partially cyber-converted (COMIC: Prologue: The Second Doctor) and led the Cybermen to their victory. This timeline was eventually unwritten by Rassilon and the Twelfth Doctor. (COMIC: Supremacy of the Cybermen)
Undone events
While aiding an archaeological team on Telos, (TV: The Tomb of the Cybermen) a Cyberman time squad attacked the Doctor. This would have killed him if their Controller didn't order them to stop at the risk of erasing their future invasion of Krelos due to the unwitting role of the Fourth Doctor in that plan. The Second Doctor then witnessed a Krelos robot drone decontaminate Jamie before time was reset and this interlude didn't happen. (AUDIO: Return to Telos)
In a negated timeline, the TARDIS was attacked on 23 November 1963 by a conceptual bomb bought by the Decayed Master and began to be erased from time. The Second Doctor, along with his first and third incarnations, became trapped in another dimension, and tried to warn their other incarnations by reducing the explosion to a blinking light on the TARDIS with the coordinates of the explosion. However, when their four successors followed the warning, the Master took direct action in attacking them, until the Sixth Doctor managed to bring them together to formulate a plan. After the Fifth Doctor ensured that the TARDIS would not explode, the Doctors prepared to time ram the Master's TARDIS. However, rather than kill the Master, the First Doctor instead turned off the automatic distress actions, making it so none of the Doctors followed it into the explosion and undoing the events of the day. (AUDIO: The Light at the End)
Parallel universes
In the Unbound Universe, the Second Doctor had twice met the Brigadier in the 20th century, aiding him against the Robot Yeti in one of their meetings. The Doctor was eventually detained and tried by the Time Lords. As punishment for violating the non-interference policy, the Doctor was forced to regenerate and was exiled to Earth in the 1970s, though his successor would only arrive in 1997. (AUDIO: Sympathy for the Devil)