I actually own both versions of Axis and Allies. I absolutely LOVE this game. It has literally replaced Risk as my go-to strategy board game (with Stratego now as a close second). I like the original version, but the artillery and DDs were a welcome addition.
I don't have any real interesting stories of civ caliber. I had a great game once as Russia, I wound up withdrawing back to probably two provinces, Moscow and Cacausus, for a long time. America beat up on the Japanese for a while, and Britain had built a nice navy and blockaded Germany on the mainland. Germany, in the meantime, proceeded to overrun all of Africa. America eventually forced Japan to withdraw back to their home islands; America was unable to invade, but settled for a naval blockade (six battleships!) It was pretty neat, because Britain built all the transports for America, and shipped both their armies to France. When Germany was suddenly faced with a two-front war, I staged a break-out, and took back all my land, with interest. The game basically ended when we had Germany and Japan isolated in their capital provinces, and the German player flipped the board in the air. We proceeded to get piss drunk afterwards, our spoils of war. Yes, that was a good plunderin'.