Krakatoa was a volcanic island in the Indonesia archipelago in the south Pacific Ocean. It erupted in 1883.
Some time prior to his third incarnation, the Doctor witnessed the eruption. During this event, he also heard Primords scream for the first time. (TV: Inferno)
That same day, a sketch of the Ninth Doctor washed up on a beach on Sumatra. It eventually found its way into Clive's collection of artefacts related to the Doctor. (TV: Rose)
The Tenth Doctor and Rose Tyler visited Indonesia, where they encountered the alien Chalderans. They were captured and hung upside down, but the Doctor used his sonic screwdriver to free them. They escaped in the TARDIS just as the volcano erupted, killing the Chalderans. (COMIC: Under the Volcano)
The eruption also caused a Xylok to be freed; this Xylok became Mr Smith many years later. (TV: The Lost Boy)