They're not illegal to own in many places, US included.
In the United States, the law against selling fake bags is the federal trademark law also known as the Lanham Act. Trademarks are names, phrases, designs or marks that identify the source and manufacturers of products. Each state also has its own trademark laws, as do most countries outside of the United States.
Go to www.dhs.gov (homeland security) and search "counterfeit handbags". See what the U.S. government says about it and why they are arresting people that sell them.