Christmas crackers were an integral part of Christmas parties. They were pulled by two people and there was a resultant bang. They commonly contained novelty gifts and hats.
The Tenth Doctor once pulled crackers with Rose and Jackie Tyler while dining with them at Christmas. (TV: The Christmas Invasion)
On Christmas Eve, the Eleventh Doctor pulled crackers with the Pettigrew family and Kazran Sardick as part of their celebrations. He hid a playing card in one. (TV: A Christmas Carol)
Clara Oswald had a cracker at her family's Christmas celebration, but later took it to an aged Eleventh Doctor on Trenzalore. (TV: The Time of the Doctor)
On Puxatornee, Professor Capra asked the Seventh Doctor and Mel if they wanted to pull a cracker. (AUDIO: Flip-Flop)