Translation for "sorry" as in "I am sorry to hear that"?
Sorry has many meanings in English while 对不起 doesn't do that in Chinese. Most of the case, you can use 不好意思 - it'd be more easy-going and it's a little like "sorry" in English sometimes.

So for different context you need to say different words. Some examples for you:


不好意思 - It's very general and can fit many situations. I recommend use it when you're not very sure. 


  不好意思，我不知道你们已经离婚了。I'm sorry that I didn't know about your divorce.

抱歉 - feel bad when you mention something that your listener don't want to hear


  抱歉，我刚知道你父亲去世的消息。I'm sorry I just knew that you father passed away.

难过 - feel sorrow about something (stronger emotional than the two above)


  听到这个消息，我很难过。I'm sorry to hear that.

伤心 - feel rather bad about the loss, especially someone loses his a family member. But it's a little formal than 难过. You can use it in a letter or e-mail


  得知你要离开这个城市，我真的很伤心 It's so sad to realize that you're leaving this city.

遗憾 - it's a little formal and official, I do not suggest use this in a daily conversation. Chinese people seldom say it.


  听说你不打算加入我们了，我感到很遗憾 It's a pity to know that you're never gonna join us.

惋惜 - the same like 遗憾, it's very formal and seldom used in daily conversations.


  关键时候没能坚持住，真令人惋惜 What a pity that you did not hold on at this crucial moment.

悲恸 - it's much more formal and official, for example when some "big brother" in the gov is dead the media will use this word to report


  毛泽东逝世后，举国上下沉浸在极其地悲恸之中无法自拔。 Every single person in this country has broken his heart after knowing Chairman Mao has passed away.