It is perfectly normal here to apologize except that the apology comes in different forms. For a Chinese to apologize directly would mean that he did something very wrong. For instance, if there was an accident and two guys came out arguing, finally one of them accepts that he has to pay for the damages, meaning he agreed that he was wrong, but he will never outwardly say sorry. It's face thing. The most he will say is "bu hao yi si". People here are confused when we apologize openly because it's not their culture to do so. Sometimes, they feel awkward when we do that and they do not know how to react. Quite funny actually. But I will always apologize even for the smallest mistake. I guess it's in us to say sorry, thank you and please. I don't think we should change that just because they don't do it. 

yes, to my wife, and sometimes to some strangers  ... no need talk about reasons, do I ?

Indeed, apologizing it's a sign of weakness.

When you do so, you're mostly defeated and you're looked upon as an easy prey.

To Chinese people, the Western Cultural understanding of showing your feelings, it's opposed to the Chinese meaning of strength of character. To us, the people educated in a cultural environment based on Christian values, showing that you're sorry it means, to some extent, making yourself vulnerable.

 There is a Chinese way of apologizing in the way that you protect the offended's  emotions from feeling embarrassed with your display of  vulnerability when you apologize. 

It looks that the Western style of expressing feeling of sorry it puts the Chinese people in a situation of shyness. Any display of emotions in such circumstances, it's understood as weakness and it can't but confuse them or even worse may reject you in a way or another. 

I tend to believe that the attitude expected is that the offender should show an attitude of protection towards the offended one, meaning towards his feelings and the best way to do would be not showing up emotionally rather than making your point in a simple way possibly.  

I must admit that to me it's still a lesson about what Chinese' soul map is and how emotions and thoughts connect each others. I myself have been confronted with negative responses, no matter how genuine and sincere would be saying that I was sorry. 

Apologies are seen as irrelevant. My wife tells me that if I were truly sorry, I wouldn't have let it happen. There wouldn't be something to apologize for if it didn't hapen, but logic never gets in the way in China. I get the impression that that's the prevailing sentiment here. Epecially nowadays on the streets, acknowledging error is weakness, and people take advantage of that. A perfect example I can think of, was some guy coming out of the toilet and accidentally switching off the lights of the entire restaurant. He doesn't make the effort to switch the lights on again, and gives no sign of noticing that he's the reason there is almost complete darkness in the restaurant now. He walks on proudly in the dark as if no error had occurred. A waitress had to stumble towards the toilet area and switch the lights on again. Mianzi/facesaving; love it or hate it... it can be funny on occasion.

I remember I the first time I came to China, I was at a super crowded mall in Shanghai where I accidently, though forcefully bumped into a child (maybe 6-7 years old). Saying sorry was one of the very few things I knew how to say in Chinese back then and I apologized to both the child and the mother. The child didn't seem to care, and the mother looked at me like I was a complete idiot and rushed away. I was left scratching my head, since the the way I have been raised "sorry" and all the other polite words, thank you, please etc are super important.

And like coineineagh said, I've also been told that if I was really sorry I wouldn't have done whatever I've done by my fiancee back when she was my girlfriend. Although now we understand each other better, and what sorry means for me and for her.

Saying you are sorry, when acknowledging a wrong-doing as well as an accident, is something i still do automatically. In addition i still thank people as a matter of common courtesy. 

I was told by a local friend that neither were necessary. In fact thanking people as often as i did was only something that beggars on the streets here did.

it may be against the local culture, but there is some cultural brain-washing i can't over-come.

that and my mother would hit me for showing poor manners 

Here is what pisses me off:

If they are wrong and should apologize it means they lose face and an apology is never forthcoming. It may get to the point that they start yelling in retaliation just to mask the problem.

If I am wrong and do apologize they take that as a sign of weakness and will exploit that for as long as humanly possible.

Beware! Trying to "reason" with most Chinese people is a no-win situation.

When I've apologised for something I've done, I've usually heard "meishi", and that's about the end of it.

From that, I figure that Chinese are aware of our culture, and get that we have these 'manners' things, where 'please', 'thank you' and 'sorry' are norms.

Also remember, even in our culture, saying 'sorry' is a sign of accepting responsibility - and thus, it's advised by police not to say sorry at an accident, as it infers legal responsibility. (obviously, there are good times just to get that out of the way, but it shouldn't be so automatic, otherwise you can be taking responsibility for something you shouldn't be!!)

I also think, like those above, that it's a part of our culture that we shouldn't be changing!  If others see us as weak, then perhaps they'll find out the hard way how we're not!

be careful with apologies in China.  An apology will get you slung with a disproportional  amount of guilt. basically you'll get stuck shouldering blame for other things that may not have been your fault.  Locals seldom apologize and you should be careful about how and when you apologize as well.  Guilt admission means you are going to shoulder the blame for 100% of whatever it was.  There's the added element of shaming here.  Apologies are not merely apologies.  They can and will be used against you.

Your good manners can't change chinese. Why should you let chinese change your good manners? Say all the "thanks" and "sorries" to your heart's content. Being foreigners, we can get away with cultural differences.