In some situations, an apology can equate to an admission of guilt. If there are any concerns about the repercussions of an apology, you may want to consult with your legal department before making it.

Some business people employ underhanded or downright illegal tactics in their work. If you are pressured to do the same and refuse, there is no need to apologize. Your personal integrity is more important than smoothing over a stressful situation.

If you are wrongly blamed for a mistake, make your case and speak up for yourself. 

You may be tempted to cover for others, and while helping someone else out of a tough spot may seem noble, this could eventually evolve into someone using you as a doormat, or esc...