Some of the most misplayed hands in Texas Hold' em are the starting hands of Ace/Queen and Ace/Jack. The reasons are many, but let's look at one or two examples.
The game is No Limit Hold' em. The blinds are $5/$10. (The blinds can be anything you like, but for our examples we will use $5/$10 blinds.) You are in early position (under the gun,) and raise into a pot that is already $15 (due to the blinds.) You put in a standard 3X raise of $15. The next few players fold until a player in late position (the cut-off) calls. Then the button raises another $30. The pot is now $75 and it's your turn to act. You need to put in $30 to calls.
You are already in bad shape. Having one caller, and then a raiser who is making a raise, (knowing that someone just called a raise in front of him,) puts you in a difficult position. If you call, you have to worry about the player who originally called. If he calls again, you are most likely in third place before the flop. He might even raise or push, all-in. So what do you do? Of course the answer to most poker puzzles would usually be: "It depends!"
Is the player on the button a super aggressive player, who might raise you with a pair of deuces? Does he have a huge stack, and may no care about the money? Is the player right behind you, a solid, tight, player who is going to fold a wide range of hands if you call? Without going into the five hundred different things that might happen here, you can see why your hand is much weaker than many amateur players might think. In fact, all things being equal, and having limited information about these players, my play would be to fold.
Because you have a raise after the first caller, (making the raise less likely to be a bluff) and because you will play the rest of the hand out of position, I would recommend a fold.
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Let's look at the same hand, but this time the player on the button just calls and everyone gets to see the flop. There is $60 in the pot, (the blinds, your $15 raise, and the two $15 calls.) The flop comes A-K-9 rainbow. In most games, you should bet here, to protect your hand and keep the lead. So you bet $40, making the pot now $100. The player behind you calls and the button raises. What do you do?
Chances are, you are once again, in third place. You have a player behind you, yet to act, who could have been looking to check-raise. Both players have played the hand so far, as if they have AK, KK etc. You might even be up against 99 giving a player a set. The chances of you being in the lead here are slim.
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So how do you get yourself out of such a situation? For starters, you can avoid the hand overall. AQ in early position in a loose game, is not a great hand. In a tight game, you can raise and hope to win right there, or maybe with a continuation bet on the flop.
The bottom line is: Consider the nature of the game, who is sitting behind you, and your table image, before getting stuck with this hand which often leads to you being put in a difficult decision. Especially out of position.
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It should also be noted, that you will not find many world class players folding this hand, even from early position. But also keep in mind, that world class players are going to make much more astute decisions after the flop, therefore they are able to get involved in many more hands than the average armature player.
