A temporal collision occurred when the Tenth Doctor inadvertently caused his TARDIS, which he had neglected to shield, to crash into that of his fifth incarnation's, which put the universe in danger of being sucked into a Belgium-sized black hole. However, the Doctor used his memory of the event from his fifth incarnation's viewpoint to create a supernova at exactly the same moment the black hole appeared. As a result, the Doctors' TARDISes separated and the two parted ways. (TV: Time Crash)
The First Doctor's TARDIS collided with the Second Doctor's in the Time Vortex which broke vital control circuits in both TARDISes, stranding them on Urbinia. This resulted in an alternate timeline in which the Daleks successfully developed the Time Destructor due to the First Doctor's absence from Kembel. After repairing his TARDIS, the Second Doctor used the fast return switch and deactivated the temporal safeguards, to avert the initial collision. Zoe Heriot feared this risked a dangerous paradox but after the resulting temporal storm dissipated, the First Doctor's TARDIS landed on Kembel and the original timeline was restored. (AUDIO: Daughter of the Gods)