According to an article on the website Slate, the answer is yes—although many stores don’t actually enforce the rule. Posting a prominent sign creates a contract, lawyers say, and by entering a shop you implicitly agree to it. Even in the absence of a sign, shoppers can be sued for negligence if careless behavior results in a broken item (if you trip over a shoelace and destroy an expensive vase, as happened in one British museum in 2006).
In practice, though, many stores simply write the object off as a cost of doing business (with a few stern looks at the customer, probably). In the case of a really expensive item, a lawsuit isn’t likely to recover the value of the item: The Slate article notes the case of a Picasso painting worth $120 million that a museum visitor accidentally tore a 6-inch hole in.
Though the museum could have sued, it opted not to, presumably because the average museum-goer doesn’t have that kind of pocket change.