Apologies are good. If I screw up, I need to apologize and try to make amends. Riffing on Seth Godin's take on dinner speakers: if you find yourself constantly having to apologize, maybe you should stop. Don't stop apologizing, stop behaving in ways that cause you to have to make amends.
We all know people who fly off the handle or say something rude to you, then apologize. After the third or fourth iteration, you find yourself thinking, "Don't be sorry, be quiet!" People who find themselves constantly apologizing (or leaving people feeling like they ought to do so, anyway) generally have a problem, and it's not the people around them. If everybody says you're a jerk, you probably are. We shouldn't apologize for being jerks; we should endeavour to not be jerks.