Anything involving shuffled cards, dice, shuffled tiles or any other randomizing element is partly based on luck; the skill involved is the skill of making the most with what luck hands you. As others have pointed out, skilled players can essentially override the luck component, but anything that has even a small element of luck cannot be said to be based purely on skill. As pointed out by others, chess and checkers are of this type, since the state of the board at the outset, and all subsequent states of the board are based solely on decisions made by the players. Connect Four and tic-tac-toe are other examples. If you can think of any other games in which all players are given the exact same playing pieces in the exact same arrangement at the outset, in which no dice or shuffled things are used to determine the movements of game pieces, I would say that game is based purely on skill.
If you go beyond the board game model to physical games, such as throwing, running, or shooting games, luck is a very small component. However, due to varying environmental factors, I would not say that such physical games are completely devoid of luck factors.