Some great games to play:
tournament-wise:
Gomoku (just puts stones down in squares until somebody gets 5 in a row...simple, yet surprisingly fun), or if your students are clever Renju is a similar game with some rules that try to balance Gomoku, as theoretically there is a player#2-never-wins strategy for player#1 in Gomoku.
sorta-tournamenty. (could be tournament-run, but there is a large luck factor...hard to "win" unless you're dealt good cards):
Oh Hell (though it also goes by the name Down and Up the River, which is more school-friendly). The wikipedia page here is pretty compllicated, but basically here's what happens: Deal each player (3-8 players is fine) X cards, then reveal a card from the deck which determines trump. Starting with the player to the left of the dealer, each player bids the number of tricks they think they will win. The dealer bids last, and it is their duty to make sure that somebody is wrong (that is, the total tricks bid cannot equal X). Then play of cards starts with first bidder; players must follow suit, and the trickWinner leads to the next trick. Easy-scoring too. if you bid incorrectly (-5)*(number of tricks off...above or below). If you're right (5) points for being right and then (5)*(number bid). But you gotta be right to get that x5 bonus.