People (myself included) over-index on apologizing when they actually haven't done anything wrong or offended anyone. I see this the most in the workplace. It's almost a knee-jerk reaction - a filler phrase to please the person that noticed or shared in your "mishap" that you think requires an apology.
The downfall of over-indexing on apology, is that instead of coming across as respectful (which is your likely intent), you can leave a less than positive impression about your professional capabilities. Not to mention, you can actually come across as disingenuous because you aren't actually stating what you really think or feel.
Here's a few tips on how to stop saying "I'm sorry" at work (and this works in your personal life too):
Replace your apology with gratitude. Instead of saying "I'm sorry" about a mishap, consider sharing gratitude instead by saying, "Thank you for pointing that out. I'll fix that right away" or "Thank you for bringing that to my attention, let's talk about that".
Share what you'll do to correct an issue. Sometimes there are things that do require an apology. Maybe something you did actually went wrong and impacted the other person. Sorry in this instance may be appropriate, but it can often be the crutch everyone leans on. Instead of saying "sorry" only, insert the action you will take to correct the issue such as, "Thank you for sharing that feedback. I will take X,Y,Z action right now to get that corrected right away".
Stop apologizing for "bothering" your colleagues. I suspect we've all been there. We have something to say or a question to ask and we're worried we're going to "bother" the person we need help from. Instead of apologizing for bothering them (you aren't really), consider saying, "Do you have just a few minutes? I would love to get your perspective on something."
Apologizing may seem always appropriate and the ultimate sign of respect and accommodation. However, overuse of apologizing can leave an impression of nothing more than an insecure professional, ultimately impacting your credibility. I encourage you to give these few tips a try when your natural inclination might be to immediately apologize.