Monopoly was a board game originating on Earth.
The Fourth Doctor, Romana II and K9 played Monopoly aboard the TARDIS. K9 used the dog token. The others had to roll the dice and move on his behalf. (PROSE: The Romance of Crime)
The Sixth Doctor and Melanie Bush played a game of Monopoly. The Doctor enjoyed winning, noting that he didn't often get the opportunity to act like a power-crazed dictator. (AUDIO: The One Doctor)
The Seventh Doctor had a Monopoly game from the 1930s or 1940s in Smithwood Manor. (PROSE: Cat's Cradle: Warhead)
The Doctor was once taken by the Entity into grey space, where he was to play Monopoly. However, he left in his TARDIS while the entity decided who would go first. (AUDIO: Seven to One)