Which are Grid-based games?

I want to know which are the grid-based strategy games available for playing?
And what this games are meant for ?

There are over 30 grid-based strategy games available for playing.
Some of them includes Ataxx, Reversi, Checkers, Gomoku, Connect Four, and more...

I will explain you about Ataxx and Quad Wrangle.

Ataxx:
The object of this game is to capture your opponent's pieces by moving your pieces next to them. There are two types of moves you can make. A normal move consists of starting from a piece that you own and creating another piece one cell away from it (horizontally, vertically, or diagonally). The starting piece remains, and you capture any of your opponent's pieces that your new piece borders. A jump move consists of moving a piece you own two cells in any direction. As with a normal move, any opponent's pieces that border the ending position are captured. To make either kind of move, first click on a piece that you own, then click on the empty cell you want to move to. The game is over when all the cells are filled, and the player owning the most pieces is the winner.

Quad Wrangle: This game is similar to Ataxx.
There are three types of moves. The first type consists of starting from a piece that you own and creating another piece one cell away from it. The starting piece remains, and you capture any of your opponent's pieces that your new piece borders. (This is the same as non-jump move in Ataxx). The second type consists of sliding a piece you own any number of squares horizontally, vertically, or diagonally. Any opponent's pieces that border the ending position are captured. The third type is a drop of a piece to any empty cell. Unlike the other move types, no pieces are captured with this move type. To make a normal or slide move, first click on a piece that you own, then click on the empty cell you want to move to. To make a drop, click on an empty cell. The game is over when all the cells are filled, and the player owning the most pieces is the winner.

Reversi, Checkers, Gomoku, Connect Four, Gravity, etc are also some of the grid-based games. And there are many more.

Reversi: (also known as Othello).
The object is to capture the other player's pieces by enclosing them between two of your pieces.
You make a move by placing a piece in an empty cell. You capture any of your opponent's pieces that are in a horizontal, vertical, or diagonal line between the new piece and another of your pieces.
Every move must result in the capture of at least one piece; you must pass if you cannot capture any pieces.
The game is over when the board is full or neither player can move; the player owning the most pieces is the winner.

Checkers:
The object is to remove your opponent's pieces or prevent them from moving. Pieces move forward and diagonally, and can jump and remove opposing pieces by landing in the empty space directly behind them.
When a piece reaches the last row, it is promoted to a king (represented by two stacked game pieces).
Kings can move backwards and well as forwards. Whenever you can make a jump, you must do so.

Gomoku:
This is an expanded form of tic-tac-toe.
Players move by placing a piece at any empty cell.
A player wins by forming a straight line of 5 pieces horizontally, vertically, or diagonally.

Connect Four:
Similar to Gomoku, a player wins by forming a straight line of 4 pieces horizontally, vertically, or diagonally.
However, you may only place a piece at the lowest empty cell in each column.

Gravity:
A player wins by forming a straight line of 4 pieces horizontally, vertically, or diagonally.
The board has a "gravity field", which pulls pieces toward the edges or corners.
If a cell is on a main diagonal (indicated by a gray background), a piece may be placed there only if there are no empty cells between that cell and the nearest corner.
If a cell is not on a diagonal, a piece may be placed there only if there are no empty cells between that cell and the nearest edge.

Hexapawn:
The object of this game is to move one of your pieces (pawns) to the other side of the board.
In the normal game, pawns move as standard chess pawns; moving forward one square to an empty position, or capturing diagonally forward.
Berolina and Berolina Plus pawns can be used in variations of this game. Berolina pawns move diagonally forward and capture directly forward.
Berolina Plus pawns are the same as Berolina pawns, except they can also capture sideways.
For all variations, a player wins when one of his pawns reaches the final row, or when his opponent is unable to move.

Apart from already mentioned games, some of the other grid-based games includes the following:

Breakthrough / Zonesh / Glass Bead / Cats & Dogs / Moray Eels / Life

Atomic / Five Field Kono / Fission / Orthokon / Bombardment / Reactor
\
Tourney / Daggers / Fianco /....any many more

Some of my favorites are:

Diagonals

Objective - to achieve the highest score by completing diagonal lines.
Method - Each turn, each player drops a piece on an empty cell. If that piece forms a diagonal line of pieces from one edge of the board to another, the player scores points equal to the number of his own pieces in that line. Note that a single piece can complete two diagonal lines at once. The game ends when all cells are filled, and the player with the highest score wins.

Think Ahead

Method:The board is randomly filled with positive and negative numbers, and a single black ball. Player 1 moves the ball horizontally, and player 2 moves the ball vertically. Each turn, each player moves the ball to a cell with a number in it. That number is removed from the board and added to the player's score. The game is over when a player cannot move (because all the cells in the ball's row or column have been used), and the highest score wins.

Dominion

This game is a combination of Ataxx and Reversi

This is about computer games right? Then I highly suggest Galactic Civilization 2, it's a grid based strategy game that is much like the civilization series, except its based in space. Very addictive too.