Hide and seek was a game often played by children.

Tony Barker and Amy Barker were playing hide and seek when they discovered the Doctor's TARDIS, which Amy had decided to use as a hiding place. (PROSE: The Monsters from Earth)

On at least one occasion, Rory Williams played hide and seek with Amelia Pond and Mels. He hid for hours while Amy and Mels neglected to look for him as they were talking about Amy's imaginary friend. When confronted about this, Amelia told Rory that they just hadn't found him yet. (TV: Let's Kill Hitler)

When Gwen Cooper arrived at the Hub to tell Jack Harkness about a lead she found on Jonah Bevan and accidentally walked in on him and Ianto having sex, Jack said that they could have used her during "naked hide and seek." Ianto told her that Jack always cheats. (TV: Adrift)

The First Doctor played hide-and-seek with the Rani as a Time Tot, with his ninth incarnation recalling that his skill at finding her "drove her nuts". He held the Time-Tot hide and seek championship for forty-two years in a row. (COMIC: Weapons of Past Destruction)