1) Apologizing to another guy
It is understood that even the closest of friends will peeve each other off once in a while or make a minor infraction that requires atonement.
It is important to note however, that under no circumstances should one guy ever tell another guy "I'm sorry."
Guy's Code requires that the words I'm and Sorry should never, ever, ever, be used in combination when talking to another guy. PERIOD.
Apologies must come in the form of just a simple look, and the words "Dude," or "What's up," followed by a high-five of handshake and a look where it is understood that an apology is implied.
To be sure, all is forgiven, it is appropriate to ask, "We cool?"

2) Apologizing to your girlfriend/woman you are dating
Again, the rule is you never utter the words, "I'm sorry."
Should your girlfriend be angry at you for something she perceives you have done wrong or if you have actually done something wrong, the apology must can come in the form of some flowers or a card or both.
The card can have the word "Sorry" written inside, but you should never utter the phrase. It is appropriate to ask her, "Did you get the flowers," or "What do you think of the flowers I sent/gave you?"
You are also allowed to use technology to covey your apology. Therefore, a text message or a brief e-mail is allowed to contain the phrase "I'm sorry," or the more formal, "I apologize."

3) Apologizing to your wife
Only when one is married are you allowed to ever say, "I'm sorry."
However, understand it is not to be offered on the whim and only when certain conditions apply.
Should, in the course of an argument, your wife says "Fine," that is your cue to go ahead and say, "I'm sorry." I have recently discovered as well that for the younger generation, women have exchanged the snorty "fine" with "whatever." So, for those under 30, the same rule applies.
It is also appropriate in such situations to say, "You are right dear, I'm sorry."
Mind you, that you are not saying, "You are right dear, I'm sorry," because you were wrong or actually apologetic, but rather as men who must assume the role of being the reasonable person in the fight and end it by falling on our emotional sword.
You are also allowed to use a version of this apology in which you actually don't assume any legal responsibility for being sorry or admitting you were wrong. In those cases, "I am sorry if what I did (said) made you angry," is acceptable.
Now, if after falling on your sword, if she remains angry or worse - withholds matrimonial whoopee - then more drastic measures are required.
You are then released to not only say, she is right and that you are sorry, but also you are allowed to actually mean it.
And in such cases flowers and a card are appropriate.

4) Blanket "I'm sorry" This one comes from For Men Only special contributor Trey Boring. It's a piece of advice he got from his dad and is an appropriate rule under certain conditions.
Now, for men who have been married for 20-plus years, there is a little known caveat within the apologizing to women rule. This rule, which only applies for men who are at least 65-years-old and/or married for 20-plus years.
Those who fall into this category are allowed to start and end their day with a blanket apology. In such cases, the man is allowed to say, "I'm sorry for anything I might do today that will peeve you off." He is also allowed to end the day with a similar saying.
What's the beauty of this blanket apology is that it doesn't matter if your wife is even within earshot or not.

5) The apology of last resort
Of course, every argument with a women always risks of escalating to a level where the man will inadvertently blurt out the one word a man is never ever, ever, suppose to call a woman.
First, men, should refrain from ever using the word, but should it slip out there is only one way to even start to fix what has been broken: Jewelry. VERY expensive Jewelry starting at 1 Karat minimum.

SOMETHING TO REMEMBER

6) Women never really apologize
There are certain facts in life. Death, taxes, the infield fly rule and the fact that a woman never really apologizes. She may make you think she is apologizing, but in reality her apology is little more than a way for her to blame the whole argument on you.
You know what we mean, "Honey, I'm sorry, but you just make me so angry," or "Honey, I am sorry, but I can't help but get angry at you when you do that."
See, they are cunning people these women. Again, always remember that women never apologize, they just find a way to blame you for everything.
To which your answer is, ""You are right dear, I'm sorry."