すみません sumimasen is probably the first word that comes to mind to apologize in Japanese as it actually means “excuse me” or “sorry” in numerous circumstances.
It is certainly one of the most frequently repeated words in Japanese conversations, especially as it can also be used to express thanks in certain situations. You may therefore repeat it as often as you please.
It has an interesting etymology, being derived from the verb 済む sumu which means “to complete, to draw to a close”. Thus sumimasen literally means “it is not over” in the sense “there is some further need”. However, its Kanji form does not have the same casual meaning.
In some specific situations, one may use 失礼します shitsureishimasu, for example, to somebody (who is) standing in your way.
For the sake of accuracy, one may combine it with the て form of verbs and therefore use 遅れてすみません okuretesumimasen to apologize for being late.
ごめんなさい gomen nasai is used instead of sumimassèn’ to apologize after the fact, for example if you have jostled someone or failed to attend/missed an appointment.
With friends, one may simply use ごめん gomen or ごめんね gomen ne, and attach the prefix 本当に hontoni (“really”) to add emphasis.
When you are visiting someone, it is better to use お邪魔しますojamashimasu (“I am sorry for the disturbance”).
These expressions may be used in casual situations. At work, however, or to people of a higher social status, you should use more formal phrases such as 申し訳ありません moshiwake arimasen or even 後悔しています kokaishiteimasu to imply that you feel sorry.
Of course these expressions always go hand in hand with a measure of body language, in particular:
- A hand raised vertically in front of your face to push through the crowd or make your way between two people;
- The inevitable bowing that goes with excuses.
Finally, it may seem funny, when one is simply looking on, to see Japanese people gesturing and using body language when they are talking into the phone with someone who cannot see them!