I know some players would disagree with my play, but, yes, I have folded AA more than once! In the same circumstances, I would fold AA again.
In one of the circumstances that I am talking about, I was on the bubble and I intentionally folded from a late position in order to finish in the money rather than to take a chance on being eliminated. It worked, and I survived to end up in the money.
In another circumstance, I was not on the bubble, but I folded AA. My reason for folding: despite my high raise and re-raise pre-flop, and despite my high raises on the flop and turn, four players came to the river with me. The community cards, and the cards that flopped on the turn and river had not increased the value of my AA, but they opened up a real possibility of much stronger cards for my opponents. So, I folded my AA on the river, and, as things turned out, had I not folded and gone all-in, I would have lost my entire bankroll to a middle straight. Lesson learned, but, at least, despite my losses, I remained alive in the game.
I am now very careful with AA, especially when following my own raises and re-raises - I notice that there is going to be a crowd at the showdown since that is how AA is most likely to be cracked. My experience with AA is that it is more likely to be cracked when more, and not less, opponents go to the river. Ditto for KK and QQ.
In case you are interested, here is more info about AA from my point of view:
Some writers put AA in the same win category of hole cards as KK and, to a lesser degree, with QQ. I do not. According to these writers, the win percentage for each, is about 83%. In other words - 8,300 times out of 10,000 hands played, these cards will win. Conversely, there is a 17% chance of losing everytime you play these cards. So, 1,700 times out of every 10,000 hands played, these cards will lose.
Based upon my own playing experience, I put the win percentage of AA higher at 86% and the win percentage of KK just slightly lower at 85%. But, I do agree with other writers that the win percentage of QQ is 83%. Conversely, I put the loss percentage of AA at 14%, the loss percentage of KK at 15% and the loss percentage of QQ at 17%. That means, just to go through the statistics, that AA will win 8,600 times out of every 10,000 hands played, that KK will win 8,500 time out of every 10,000 hands played, and that QQ will win 8,300 times out of every 10,000 hands played. Conversely, AA will lose 1,400 out of every 10,000 hands played, KK will lose 1,500 times out of 10,000 hands played, and QQ will lose 1,700 out of every 10,000 hands played.
The normal way of playing AA and KK and QQ as hole cards is fairly similar, and that is to aggressively bet pre-flop, raise pre-flop and to re-raise pre-flop where possible. This aggression should normally continue throughout the flop, turn and river. So, if you do lose on these so-called monsters, the loss is probably going to be a big one in terms of chips. Conversely, if you do win, the pot will usually be a huge also.
Now, it must be understood, that winning or losing, respectively, can happen all day long because win and loss percentages cannot actually predict "when" these cards will win or lose, only that they will win or lose a certain percentage of the time per every 10,000 hands played. So, strange as it is to say, because the "when" of it cannot be predicted, then neither a win nor a loss can be guaranteed when playing with cards like AA, KK or QQ. Just something to remember when playing these cards.