Have you ever met those folks who are as nice as can be, and they constantly apologize for the slightest little things? I've encountered people who apologize incessantly for any reason like appearing in a doorway at the same time as you or needing to share counter space in the break room at the same time. It's very thoughtful, but in and of itself, it is awkward and uncomfortable. No one did anything wrong in any of those cases, but someone felt the need to apologize.
I find myself feeling sorry for "The Apologizer" and hoping the person doesn't feel sorry for his existence. The tendency to apologize isn't anything we can change about a person, though I want to let those people know I'm not going to be upset or hurt if they don't apologize for walking down a narrow corridor along with me.
If "The Apologizer" is someone close enough to you, it's probably a good idea to let the person know of their apologizing habit in effort to make your friend a little more self-aware of their perception. If it is important enough to the person, they will make strides to self-improve a little, or they may be completely happy as is, and continue on as usual. Though it's challenging to offer feedback to a friend, they may appreciate you being a sounding board for them in the long run.
As I was thinking about this personality trait, I was curious if any others have had similar experiences. Rhonda Shasteen, my mentor, has a great point that you can't control others words, thoughts, or actions. Maybe there's a gentle way to let people know they don't have to apologize to you, or maybe apologizing is simply in the core being of "The Apologizer". If so, simply, smile, accept the apology, and move on.