Apologising

During the course of daily life there are many situations in which we will have to aplogise. Maybe we step on someones foot, or bump into somone or our baggage hits some one has we walk past. In these cases it is best to say promptly:
ああ、どうもすみません。　－　 Ah! doumo, sumimasen.　－　Oh! excuse me.
If you are late for a meeting, for example you could say:
おそくなってすみません。　－　Osoku natte sumimasen.　－　I'm sorry I'm late.
Or else:
れんらくできなくてすみません。　－　 Renraku dekinakute sumimasen.　－　I'm sorry I couldn't get in touch with you.
With close friends you can simple say:
ごめんなさい。　－　Gomennasai.　 －　Pardon me.

Other phrases are has follows:

どうも、すみません。　－　 Doumo sumimasen.　－　I'm sorry.

どうかお許しください。　－　どうかおゆるしください。　－　Douka oyurushi kudasai.　－　Please forgive me.

本当に申し訳ございません。　－　ほうんとにもうしわけ ございません。　－　Hontou ni moushiwake gozaimasu.　－　I'm awfully sorry.

失礼 いたしました。　－　しつれいいたしました。　－　Shitsurei itashimashita.　－　I'm sorry.

どうい たしました。　－　Dou itashimashita.　－　That's all right.

私の方こそすみません。　－　わたし のほうこそすみません。　－　Watashi no hou koso sumimasen.　－　No, that's my fault.

Remeber that in Japan it is considered proper to acknowledge one's mistakes and apologise.