In an aborted timeline before Big Bang Two, on the same date, (TV: The Pandorica Opens) the Kovarian Chapter of the Church of the Silence created a temporal paradox by triggering the explosion of the TARDIS and caused cracks in the universe, which were the cracks the Time Lords had been sending a message for the Doctor on Trenzalore, to which the Silence did not wish the Doctor to answer and had been the reason the Silence had gone back along the Doctor's time stream to blow up the TARDIS in the first place. (TV: The Time of the Doctor) If this timeline had been allowed to pass, the final result would have been a total event collapse. The Eleventh Doctor instead piloted the Pandorica into the heart of the explosion and cancelled it out, preserving his TARDIS and, and allowing a new timeline, (TV: The Big Bang) where the Doctor still heard the Time Lords' question on Trenzalore, to assert itself. (TV: The Time of the Doctor)
In 1284, the Pied Piper, in reality an energy entity from the Jeggorabax Cluster, kidnapped a hundred and thirty children from the town of Hamelin, Germany to instil fear in the populace. (TV: The Day of the Clown)
In 1890, the Eleventh Doctor took Amy Pond and Rory Williams to the recently opened Savoy Hotel for their tenth wedding anniversary. He assured them there would be no complications, only to discover there was a Zygon ship under the Savoy, and half of the staff were imposters. However, the Doctor managed to deal with this. (TV: The Power of Three)
During the Year of the Slow Invasion, the Ponds celebrated their tenth wedding anniversary. The Eleventh Doctor showed up and took them for a bit of sight-seeing on the TARDIS. They "got sidetracked," and ended up returning 7 weeks later, in their perspective. Technically, though, they'd only been gone for 20 minutes. (TV: The Power of Three)
Behind the scenes
This was one of only three instances where a new series Doctor Who television story, namely TV: The Big Bang, took place on the same day as its broadcast: 26 June 2010. The other two occurrences were The End of Time on 25 December 2009 and The Impossible Astronaut on 22 April 2011.