Is “No offense meant (taken)” well-accepted English expression?

The OED’s earliest citation for no offence is from Shakespeare’s ‘Antony and Cleopatra’, where it appears as Take no offence. On its own it is first recorded in Henry Fielding’s ‘Tom Jones’, in 1749: No offence, I hope. The OED describes it as ‘colloquial’, so you will need to judge carefully when it is appropriate, whether with the sense 'no offence meant' or 'no offence taken'. If you have any doubt, it would be wise to use some other expression instead.

For an inappropriate use, see here.

Yes, these are common set phrases used to pre-emptively apologise for something that might be construed as insulting—“no offense” is a concise way of saying “I don’t intend to insult you”. In American English anyway, they usually have the form:

—No offense.
—None taken.

Urban Dictionary and The Free Dictionary both have entries for this phrasing. As mentioned on Urban Dictionary, “no offense” is often used facetiously before or after a deliberate insult; you must rely on context to determine whether the sentiment is sincere.

Alternative wordings include:

• No offense meant.
• I mean/meant no offense.
• I didn’t mean to offend.