You would not know you were Charmed or had some other subtle enchantment cast upon you, but you'd definitely know you were confused--you're rolling to see how you act on a given turn. How could you not be aware of that? And obviously, it would be done on an "act normally" round, otherwise, you'd be too busy doing something else to cast a spell.
I don't think there's a hard and fast rule for this.
It's worth noting that if he makes his save, he knows something happened, some magic brushed through his brain but failed to take effect. That's in the book. But that might be moot to the real question.
Obviously most "Enchantment" spells cannot succeed if the person knows he's under an enchantment. For example, if you cast Charm Person on a store owner to make him see you as a good friend so he will give you a significant discount, there's only two ways to rule it: A) he has no idea this happened, gives you your discount, and never worries about it or B) he knows you're messing with his mind but is compelled to give you your discount, but the instant the spell wears off he runs to the authorities to report that you're a thieving magical criminal and now you're wanted by the law - better never go back to that town.
Using option B would make Charm Person almost useless, since it has extremely limited combat use. And the same can be said about many similar Enchantment spells.
It's important to note that these spells don't generally alter memories (except the ones that explicitly state that they do), so days, weeks, years after you get that discount, the store owner will remember giving you the discount. He may wonder why he was so fond of you, but that is handwaivable - I assume the spell provides for a "long lost childhood friend" feeling and might even fill in a few hazy background details, just enough to not turn the guy into an enemy when the spell ends.
As for Confusion, I agree with you that while you're unable to act normally, you may not know that you're confused. After the spell ends, you will certainly remember that you were confused. During the Confusion, when your head is clear, you still remember that you were confused in previous rounds but you really have no easy way to know if the spell is still in effect - did the duration run out or did you just have a lucky moment/round of clarity while the spell is still affecting you?
I would model this by not telling the player "Hey, you're confused for 7 rounds". Rather, just have him make his roll and describe his actions - definitely don't tell him the duration. If he asks why, maybe tell him "I don't know why you did that, you seem really confused" and leave it at that. If next round he gets his head clear, the player will have to guess whether the spell expired or not. He might try to dispel it or Cleanse it, or he might hope the spell is over and therefore he'll save his cure.
So, there's my long answer made longer...
I probably wouldn't even require the roll.
In his moment of clarity, the victim can clearly remember the last round, or last however many rounds, of being confused. That's probably enough right there for him to realize a Confusion spell was cast on him, even if he might not know the exact spell or the source/caster of it.
The roll would be Knowledge(Arcana) if the victim wanted to be sure. "Identify a spell that just targeted you" has a DC 25 + the spell level of the Confusion effect. A free action, but one he probably wouldn't even think about using while he was confused. I still don't think he could determine the exact duration because the duration is variable based on the level of the caster, but a clever caster could figure out that the shortest duration would be 7 rounds and if his moment of clarity happened before the 7th round, he could assume the Confusion was still in effect.
I think in general a person always knows when they've had to make a save. They know if they've succeeded or failed. That said, they may or may not know what required the save.
Here's an interesting one... someone casts an illusion. You see them cast it. You succeed at a Spellcraft check so you KNOW what has been cast. Then you roll a natural 1 on your save. You fail. You KNOW you failed. You know WHAT you failed at.
TOO BAD.
You believe the illusion. That's when your mind starts making excuses. That's when you have to role-play a character who is in a magically altered state. No metagaming. Your hands are tied.
I find charms and enchantments much the same. You may or may not know what's been done, but you may not CARE. Unless you get an "act normally" round, the point is moot. You're charmed and the caster had a GREAT reason for doing it. No reason to struggle.
So I disagree with DM_Blake's choice. Charm spells have great utility event if the charmed may come out of it upset. Charm a guard, get him to take you to the king, explain to the king how you couldn't get audience normally and are present to do X, where X is something really useful to him. Guard comes out of it, guard is angry, king tells guard to take the night off.