On prehistoric Earth, Arthur attempted to teach a caveman to play Scrabble in an effort to force them to evolve. He was unsuccessful, but the caveman managed to spell out forty two using the Scrabble tiles. Arthur and Ford then pulled letters out of a Scrabble bag at random in an attempt to find the Ultimate Question. They did, surprisingly, get a question, but this turned out to be "What do you get if you multiply six by nine?" so they gave up.
Earlier in The Restaurant at the End of the Universe, Arthur played a game of Scrabble with Trillian. The game was unfinished, but it can be assumed that Arthur was winning as he managed to place "exquisite" on a triple word score.
In Fit the Fifth, when they are on a mysterious black ship that they can't control and Trillian asks what they should do while they are waiting to get where they are going, Arthur mentions that he has a pocket Scrabble set.