TripleA

I'm almost embarassed to have learned about this thing through Slashdot instead of the 'Geek, but there is apparently an open source implementation of Axis & Allies, called TripleA. The site bills it as a "Strategy Engine Framework," and it does appear that you can modify things a fair amount, but it's always A&A, you can't use it to play anything else as far as I can tell. You can play original rules, the rules from the computer release a few years back, or the 2004 rerelease of the game, and you can do custom rules, alternate scenarios, and so forth. It doesn't appear that any spinoffs like Axis & Allies: Europe or Axis & Allies: Pacific (and certainly not Axis & Allies: D-Day, which is squad and not tactical level) are supported.

For this sort of project to exist, the game generally needs to either be simple, or it needs to have a massive following (I'll ignore BrettSpielWelt, I'm thinking wargames and American games here). Axis & Allies certainly has the fanbase. For games that don't, there are more generic solutions available like VASSAL (Java) and Cyberboard (Windows only). These really are more like toolkits or frameworks, as they don't enforce rules, but instead exist as a sort of virtual tabletop. They support the notion of "cards" and a "board" and "dice" and other common things, along with tools to move pieces, roll dice, hide cards, etc., and people have created graphics and config files to play particular games, but it's up to you to remember that you can't move a piece from Australia to Kamchatka in one turn, or that you need to roll a 3 to do action X.