The Radio 4 programme Word of Mouth last week looked at the language of apologies (I'm afraid I only just caught up with it on iPlayer today, so although you can listen again here, you've only got another day to do so).
The conclusion reached was that most English speakers are not apologising at all when they say 'sorry'. What they are really doing is regretting that something has happened, but are not taking any responsibility for it. Politicians are the worst offenders (saying things like "I'm sorry people feel upset", or saying "we are sorry ..." thus distancing themselves from any responsibility).
There is a big difference in the way English speakers and Russian speakers apologise, and the linguist who was interviewed in the radio programme had devised a study based around a context where someone had been asked to look after a friend's goldfish while the friend was on holiday but the goldfish had died. English speakers (I can't remember now, but it was probably Britons who were meant) tended to shy away from accepting any responsibility even if they said "Sorry". They said, for instance "Sorry, I don't know how it happened". Russians appeared to be mortified and expressed this in their words eg "Sorry, I have not been a very reliable friend".
English speakers use the "I" form of the verb, namely, "I am sorry", whilst in Russian it is the "you" form of the verb that is used (imperative), namely "Forgive me" (izvinite or proshchaite).
I have noticed similar patterns in other speech acts -- English speakers use "I" and Russians "you". For instance, in English when asking for a favour we might say "Could I borrow your pen?", "Could I speak to you for a minute?" or "Could I possibly have a lift?", whereas Russians would say "Would you give me your pen/ a lift?" etc. (Admittedly in English we say "Have you got a pen?", but this is not a direct request).
The next edition of Word of Mouth is devoted to grammar, so there might be something in that worth listening too. See the programme's site.