Hide and seek was a game often played by children.
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)
The Seventh Doctor agreed with Chris Cwej that the TARDIS was "the number one place to play hide and seek in the universe". Nevertheless, Roz Forrester refused to play with Chris. The Doctor called Roz a fool for declining. On one occasion, Chris was told to hide; she said she'd come to find him later, but never did.
When it came time to say part ways with Eleanor Blake, Chris instructed her to close her eyes and count to ten. So that they would not have to say goodbye, the TARDIS would be gone when she re-opened them. (AUDIO: The Jabari Countdown)
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)