Trust me...Xeda made mistakes in his theory and argument..... 

Question

I often see notice/clause such as "once broken considered sold" being displayed on shelves especially glassware.

Am I legally bound by such notice, as a consumer?

What are my rights? Can I outright reject it against the cashier if I accidentally broke one? Am I obliged to pay?

Do advise a case or two so that I may refer to and learn from it.

Answer

An interesting question, and I'm not entirely sure I know the answer.  Fortunately, I haven't ever had to find out first-hand!  A contract requires a meeting of the minds, that is, an agreement amongst the parties.  You haven't agreed to anything; although, a better worded sign from the retailer's side would be in large print, posted at the entrance and say something like "NOTICE: SHOPPERS ENTER AT OWN RISK AND ARE RESPONSIBLE FOR ANY MERCHANDISE BROKEN".  So arguably you are not bound, especially if you exercise reasonable caution in the store and tragedy befalls nonetheless.  If you are negligent or reckless in your behavior in the store, you are likely going to be responsible. 

The long and short of it is that just because the sign is there, that doesn't answer all the questions, whatever the shopkeeper might think.  Likewise, with the fine print on the back of valet tickets, parking ticket stubs, admission tickets, etc.  Most people believe they are bound by these terms they have no ability to negoitate and that they sometimes are not even aware of until after something has happened; however, in many cases these have been held ineffective by courts.  I am not aware of a specific case on the "Break it, pay for it" signs, but there may well be one out there.  Of course, you didn't specify your state and this could vary from state to state.

I hope this helps a little, though, of course, I don't profess that it's "the answer".