All purpose products

I came across this interesting post at Insight & Ingenuity, which poses a great question. Can you have a product on the market without targeting it at one specific customer base? They think that if it's positioned right, it could work, but only if the customers connect with the brand. In this case, it's important for a company to reach out to the customers and find out what really matters to them.
Do you agree with this? Can we come up with one product that suits an entire market?
Note: The title of this post has been updated