Express your remorse because you've genuinely grown, not to manipulate and pacify.
Done properly, saying "I'm sorry" is a beautiful thing. It does, after all, take courage to admit that you had a negative influence on someone else. But if you spew apologies too profusely when they aren't really warranted, you actually can corrode how well people think of you.
Here are a few cases when saying "I'm sorry" isn't called for:
1. You need authority
Women are often guilty of this one, but it often happens to new hires or those with less experience in their careers, as well. You may say "I'm sorry" as a quick preface or interjection when you are asserting yourself or expressing your opinion, simply because you don't yet feel qualified or equal to the others in the room.
This can make it even harder to get fair treatment, because others subconsciously accept that, based on your own cue, you're not ready to play at the top. As long as you do it politely and have your facts straight, be assertive and claim your right to speak.
2. You don't feel remorse
Some people say they are sorry after an offense simply because others demand it as a result of social norms. But if you apologize without really feeling regret or before you grasp how the other individual was offended or hurt, you'll come off as an insincere phony no one can trust. A late, heartfelt apology offered with real sincerity is always better than a hurried, hollow one said only because others say you must.
3. You're not the real offender
It happens all the time--decent people purposely taking the fall for things others have done to protect them or the company image. In the worst situations, others might even pressure you to apologize and take the hit. But sooner or later, the truth always comes out, and integrity means being willing to put blame where it truly belongs even when it is difficult.
4. You're beliefs are conflicted
Just because someone wants you to apologize doesn't always mean you've done something wrong. It can just mean that you've done something that someone else doesn't agree with. For example, if your religious beliefs say you should give thanks for your meal and someone is offended by your practice, you should not feel like you have to compromise your faith to make the situation right.
Acknowledge their views with courtesy, but hold firm to your personal values, doing your best to share, learn and build the relationship in the process.
5. It was just a simple, everyday accident
Whether you bump into someone or spill your coffee on your teammate's new suit, "accident apologies" are simply an attempt to acknowledge that you made an honest, human mistake.
You can do this well without the "sorry" that gives an impression of submissiveness. Instead of "sorry," acknowledge the reality of what happened, such as "Oh, I was just going way too fast!", or "I was trying to do this when I was too tired to focus." Then follow up with an offer to right the wrong, such as "Can I pay for your dry cleaning to get the stain out?" or "Let me rearrange my next few calendar items and I'll make sure to have the numbers corrected for you in an hour."
Sometimes, a nice gesture (e.g., holding the door for someone you bumped into) is an appropriate alternative.
You should use an apology when...
Apologies are always appropriate when your intentional actions have caused emotional or physical harm to someone else and you recognize that that damage shouldn't have happened. This means that you offer the apology not to manipulate (e.g., to pacify), but because you have grown and have fine-tuned your ethics through some tough inner work over time. Even if the growth takes years to complete, the apology still should be given if it will bring you peace to express the regret--genuine apologies have no expiration date.
The big thing to remember is that, if you restrict your apologies only to when this genuine growth is happening, they better retain their value--they do not become a cheap, dime-a-dozen event that others numb themselves to. It's the evidence of your development that people look for most as a signal you're worth trusting again, so take it seriously and don't fake it.