A long game was a manipulation of events over an extended period of time.
Weyland admitted to playing a long game when it was revealed he had saved Hex from dying at Scutari (AUDIO: The Angel of Scutari) as he was meant to be part of the secret weapon against Fenric. (AUDIO: Gods and Monsters)
In the year 200,000, the Ninth Doctor claimed someone was playing a long game when he speculated that the human race had been set back 90 years, corresponding with the opening of Satellite Five 91 years before. (TV: The Long Game) The setback was caused by the Jagrafess which had been put in power by the Dalek Emperor so he could rebuild a Dalek race from humans. (TV: The Parting of the Ways)
While not specifically referred to as long games, the Black Guardian's attempt to kill the Fifth Doctor (TV: Mawdryn Undead) and Fenric's game against the Seventh Doctor (TV: The Curse of Fenric) could be seen as long games as they extended across several points in time and space.