There are sentences in English like "What's up?" "What's going on?" "how have you been?" to begin a conversation with or to greet people (friends or relatives)
So what are the common ice-breaker sentences in Chinese?
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If you here mean "ice-breaker" is " Something that can break the ice while talking in a senario or environment that makes people very stupid or embarrassed. You can say:
1) 没和我开玩笑吧？(Are you kidding？！)：Used when you feel ver surprised at something or something very awful that you don't expect to happen.
2) Invite someone to have a dinner with you (Even if you are not good with someone but you wanna have a talk with him, that's what Chinese people are glad to do).
However, if you wanna know something to be used when you wanna start a topic with a man not familiar to you, here are some tips:
1) 可以借个火吗？(If you see the man is smoking, you can say this to have a talk with him for the following things). 2) 你好，饭吃了吗？(You don't need to invite him/her to have a dinner but just a greeting sentence for your following talk).