Axis & Allies is rarely played to actual victory, as one side normally gives up once they have lost a major capital. The official victory conditions have varied.

NGEMilitaryBothControl 2 enemy capitals
NGEEconomicAlliedControl 85 value in areas at end of Japanese turn
NGEEconomicAxisControl 70 value in areas at end of Japanese turn

In AAC there were 2 ways of winning. You could take 2 opposing capitals while holding your own. The Axis could win by having a total combined income of 84 at the end of a turn, called Economic Victory.

IB introduced other victory options. Total Victory involved taking every area on the board. Economic Victory became an option fo the Allies at an income of 104.

AAE simply had taking any enemy capital for victory.

AAP reflects Allied superiority by making Japan's objective simply survival. The Japanese score 1VP for every 10 points of income collected (dropping fractions and adjusting for strategic bombing). 22VP constitutes a Japanese victory. The Japanese can also win by taking Australia or India.

AAR introduced the concept of Victory Cities. There were 12 on the map. You win be holding a specified number at the end of a turn. The game length was determined by the number of cities which could be 8,10 or 12. It was quickly seen that the Axis could usually hold 8 cities in 2 or 3 turns, so an option of 9 cities was added.

AA50 used the same concept, but with 18 victory cities, 12 being required for victory.

AAP40has 8 victory cities, with 7 required for victory.

TripleA has a type of attachment to describe victory conditions

<attatchment name="conditionAttachmentAxisVictory1" attatchTo="Germans" javaClass="games.strategy.triplea.attatchments.RulesAttachment" type="player"> <option name="alliedOwnershipTerritories" value="United Kingdom:Russia:Germany:Japan" count="4"/> </attatchment>