Players: 2
Grid: any arbitrary rectangular size
Rules: On alternating turns, each player must choose a tile on the grid. When that tile is selected, every tile to the right and below it is removed (including the original tile selected). The play then continues to the second player. He moves likewise. This is repeated until there is only one tile on the game board.
Winning: The player loses when he takes the lsast tile on the game board (the upper left tile). If the player click on hte upper left tile at any point in the game, he would clear the entire board, and instantly lose. The winner is the player that forces the other player to take the last tile(s).
Players: 1
Grid: any arbitrary rectangular size
Rules: The player is given a grid with a arbitrary number of different elements (numbers, colors, letters) with one element per tile. The game board starts with every tile filled. The idea is to remove as many of these tiles as possible. Tiles are removable when they are horizontally or vertically touching another tile of the same element type. A single click on a tile will highlight the entire groupd of connected elements, and a second click will remove them. Once tile have been removed, the game board reforms itself. There is a "gravity" effect, where elements will fall down if there is an open tile below them. There is also a "sideways gravity" effect, where tile will slide to the left, if the entire column to the left of them is empty.
Winning: The game continues until there are no more possible moves. Score is kept along the way (based on number of tiles removed and number of tiles removed per turn). The player tries to beat his previous best score.
Players: 2
Grid: any arbitrary size, but almost always played on a 8x8 grid
Rules: The game starts out with four pieces in the center ofthe board, two of one color, two of the other. They are arranged diagonally from each other in the centermost "square". The first player moves by adding his colored piece to the board. His move must be made is a tile that is adjacent to another piece on the board. Additionally, the move must "turn over" one or more opponents tiles. This is done by placing his colored tile around a row, column or diagonal line of the other players tiles. Then all the tiles are flipped and become the property of the first players. The turn proceeds to the second player who plays likewise.
Winning: The game ends when all possible moves have been made, or the game board is full of pieces. The winner is the player with the most of his colored pieces on the board. If multiple games are played, the margin of victory can be kept and the winner can be the first to 50 or 100 or some other point value.
Players: 1
Grid: any arbitrary size
Rules: The game board starts with several different types of elements in random locations on the board. Each turn, the player must remove two like themed elements from tiles. For the move to be legal, the first tile must either touch the second tile, or there must be some path of empty tiles between them. When a legal move is made, the two elements are removed from the game board, and their tiles are left blank.
Winning: The game is over either when all the elements have been removed, or when a timer reaches a specific value. The player tries to beat the timer, and also his previous best score.
Players: 2
Grid: 8x8
Rules: It's checkers (I'm not typing this out). http://www.triplejump.net/usrules.shtml
Winning: The game is won when every one of the other player's pieces has been taken by the first player.
Players: 1
Grid: any size, larger is usually more difficult (provided that more mines are added)
Rules: All tile start off blank. In a given turn, the player has to click on a tile to uncover what is under it. If a mine is under that tile, the player loses. If a number is under that tile, it tells the player how many mines are adjacent to that tile (1-8). If it is blank, there are no mines adjacent to that tile, and all adjacent tiles are automatically revealed.
Winning: When all non-mine tiles are uncovered, the game is won. Additionally, the player tried to beat his lowest time from previous games.