As a PM, how accountable are you for the success of the product and the business?

Both 10% and 90%.

The product is accountable 10% because while the product need to be amazing; sales, marketing, support, bizdev, finance, etc etc all need to align and do their part to inform, package and sell the product. A great product poorly sold can't succeed.

However, the product *function* (lead by the head of product) is accountable 90% because it's his or her job to drive alignment across all other functions. A great PM knows that building a great product requires great alignment across all internal and external stakeholders (i.e. the market).