How likely are you to say you are sorry? At work? At home? In general?
A co-worker of mine shared this article with me yesterday. In For higher pay, learn to say you're sorry, the author (Anne Fisher, FORTUNE) discusses a survey done by Zogby International (hired by The Pearl Outlet) to find out about why and how people say they are sorry. An unexpected result of the study presented itself. Turns out, your willingness to say you are sorry may be related to how much money you make.
"People earning over $100,000 a year are almost twice as likely to apologize after an argument or mistake as those earning $25,000 or less, the survey found."
One of the conclusions drawn is that high earners tend to be more secure and therefore not feel that they are giving anything up by saying they are sorry. Another theory is that people who make more money are more apt to believe in the old adage that it is better to ask for forgiveness than permission.
Regardless of what the possible cause/effect correlation is, as the article goes on to point out, well-timed apologies can be very effective. Have you ever been in a situation where someone's apology completely took the wind out of a conflict situation? There's nothing like a heartfelt 'Wow, I'm really sorry" to make you take a deep breath and focus on the situation rather than the blame. By getting blame (even if it is just perceived) off of the table, it allows those involved in the situation to shift their efforts towards working the issue.
Even if the blame does not belong squarely on one person's shoulders, a well-timed and honest "Gosh, I'm so sorry that I didn't do my part. What can I do to help make it right?" can go a long way in building trust and respect between people. In fact, the willingness to take the fall for something, the ability to say "the buck stops here" is a tried and true indicator of great leadership.
Will saying you are sorry for everything get you a raise? Probably not. At least not immediately or directly. However, genuine apologies will go a long way in building trust and strengthening relationships.

