[neolog]

Good answer.

Though "ask for forgiveness" seems like a specific cultural/quasireligious thing that not everybody assigns meaning to.

[admash]

A request for forgiveness indicates that the speaker desires a restoration of the relationship that was damaged. One can have regret ones actions, take responsibility for them, repair any damage, take preventative measures for the future, and still not express any desire to go back to having a good relationship with the person. A request for forgiveness speaks to the motivation of the speaker -- whether it is an interest in the well-being of the harmed party, or merely self-preservation as an individual.

[wpietri]

In the sense of asking forgiveness from $DEITY, sure. But in the sense of saying to the person harmed, "Please forgive me," I think it's very broad.

[gknoy]

It's considered part of a "four part apology", and is often taught when teaching kids how to apologize.

    I'm sorry.
    What I did was wrong because ____
    Next time, I will ____
    Do you forgive me?

Forgiveness is not required (though encouraged), but you should still ask for it. It's not perfect, but following the pattern is something that helps one demonstrate that you understand both why one's behavior wasn't OK (and how it hurt someone else), it also communicates that you intend to change your behavior.

This blog post seems to pretty solidly convey part one, but the others less so. It's still good to see the "I'm sorry".

[neolog]

I dunno

[wpietri]

I suggest you look up the research on this.