The most common phrase in german phrase book for apology would be es tut mir leid or tut mir leid to mean "it does me suffering".
From the questions on the difference between "entschuldigen" or "Entschuldigung"
- What is the difference between Entschuldigen and Entschuldigung?
- Kann man sich entschuldigen oder nur um Entschuldigung bitten?
it remains unclear when to use which.
How do you use apology towards specific situations? e.g. "I am sorry for my late reply." in emails or "I am sorry, the person you've just asked for is not available"
Es tut mir Leidis more personal (i.e. used if someone passed away) and used to express your own grief over something (=> I'm sorry) whileEntschuldigen Sie bitteis used if you seek the acknowledgment of the other (=> Please excuse my action). – S22h Jun 17 '13 at 08:47