Axis and Allies (A&A for short) is a board game published by Milton Bradley that simulates World War II circa 1942. Up to 5 players can play the game, each representing a WW2 power: USSR, Germany, UK, Japan, and USA.
The game board is basically a simplified map of the world with large "zones" which are controlled by the various factions. Each zone is worth a certain number of points (Industrial Production Certificates, or IPCs, as the game calls it). Using a variety of military units (more on those later), players can attack opposing zones - the winner then takes control of the zone and obtains its IPCs. IPCs can then be used to buy military units or research technological improvements.
There are three types of military units: for land (infantry and armor, which is the same as tanks), sea (carriers, submarines, battleships, and transports) and air (fighters and bombers). Each unit has different offensive and defensive statistics, between 1 and 4. To succesfully cause damage, the unit must roll that number or lower on a d6.
Gameplay is perhaps a little slow. In the beginning, each turn may seem tedious to the casual player, but strategy is a harsh mistress at best. The game does speed up near the end as a definite conclusion becomes clear. There are many exciting moments, such as one lone infantry miraculously holding off two tanks, or a frantic matchup between two huge naval fleets.
There are different ways to win, depending on if you are the Axis or Allies side. Recently, Milton Bradley released Axis and Allies: Pacific and Axis and Allies: Europe, two new games based on the same basic game mechanics, but in a smaller geographical context. There is also a computer version of the A&A.