A game, often played on some sort of board, which may include any number of cards, counters, or playing pieces as well. Sometimes pure card games get lumped into the category, but TableTopGame? might be a more appropriate term at that point.
Most board games focus on IntellectualProblemSolving?.
Prolific game designer Reiner_Knizia? believes there are three ways to come at board GameDesign: mechanics, theme, or components. The final product will probably include all three, but when looking for new ideas, it may be best to focus on one area and expand from there.
A mental exercise on the part of the current author:
Wiki:ChessBoardUserInterface? discusses how changing the colors and shapes of a chessboard can make it easier or more difficult to play.