I've been playing Axis & Allies for a while and I still enjoy it. Generally my friends and I have found that the game is balanced in favour of the Allies. We play with the basic set (I have the expansion by Xeno but I have found it is even more biased towards the Allies-especially the fact that Russian infantry only cost $2 ... but that's another story) and use the Russia-can't-attack-first-turn rule and give Germany Jet Power and Japan Super subs. The basic strategy I usually follow for the Allies is below:

Russia-Build men in Russia every turn. UK-build a carrier (or the US can build one), build a transport fleet, land in Western Europe, forcing Germany to fight on two fronts. US-Ignore Japan, build a transport fleet to reinforce the British invasions of Western Europe.

I have found that this strategy works most of the time. I have read that a lot of people like reinforcing Russia with American and/or British planes, but I find them more useful for supporting land attacks on Western Europe. If Germany does manage to take over Russia, it has usually left itself too open to attack on the Western front.

For the Axis, I use the following plan: Germany-build lots of infantry and a few more tanks. Send minimal forces to Africa-ie just enough to force the Allies to waste time/money dealing with it. Hit the British fleet on the first turn, but not again since you lose your air force that way. Take over Russia ASAP, but not at the cost of leaving Germany too open. (easier said than done!) Japan-Go west! Get deep into Russia ASAP. Initially, I prefer building transports to an industrial complex, because you can use them to make the US player think you are planning a big amphibious attack on the US/Alaska, forcing him to spend money on the West Coast fleet. Meanwhile your transports can send lots of men and tanks over from Japan to the mainland (and if you get bored, you have lots of hardware/casualties for a big fun naval battle). If Germany can't get Russia, hopefully Japan can.

My friend has an Allied plan that is summed up in two words "Heavy Bombers". He just keeps developing weapons until he gets them using either UK's or US's money. Usually by about turn 3 he has them and bombs Germany into submission. We have instituted a no heavy bombers rule when he plays, because it throws strategy out the window!

Anyway, I have been trying to think of some balancing factors to help give the Axis a fairer chance of winning. One idea is to make the US spend half its income on the West Coast (and not be allowed to move it all over to the East Coast after building it) This would take some heat off Germany, and make the naval war in the Pacific interesting. I haven't tried this idea yet, (no time-exams!!!) so I don't know what affect it will have.

I would love to hear some comments/criticisms on the stuff I've written, and also some other ideas for balancing factors.