Gurney suggested parents introduce kids to a card after children learn how to spend cash within limits.

"Once they know how to regulate their spending, they will know how to pay off a card," Gurney said. "If they are off to a good start and have a good experience, these are lessons that will stick to them through life. There are so many people that really don't know how to use credit appropriately, and it's because they never developed the discipline of self-regulation."

Family money values

Whether your family lives on cash or plastic, or uses both, Alderman recommended teaching kids about your family's choices.

"The most important thing is to make sure you instill your own money values with kids. If you are a family that shies away from debt and values cash, that's fine. Conversely, if you are a family that uses cards for everything, help them understand that, too, and why you make those choices," Alderman said.

Parents set a financial model for their kids, Amin said.

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"So if your children only see you use your credit or debit card, that will certainly have an impact," he said. "We have to be mindful of how our spending habits influence our children."

Credit cards are not inherently bad -- it's how consumers use credit that can cause problems, Amin said. "It's running up debt for discretionary items where people get into trouble and it doesn't make a lot of sense," he said.

Right for your kid?

Parents can start to introduce plastic when their kids become teenagers, experts said. Amin recommended setting low limits for cards for kids.

"Let kids start small, so if they make mistakes it's not catastrophic to them or you, and let them learn to manage credit but with keeping a tight watch on how much they can spend," he said.

Not all kids will be well-suited to using plastic. "You have to be honest about who your kids are," Alderman said.

Parents who aren't comfortable with their kids having a card should still talk to them about the differences between payment vehicles.

"So many kids just see a piece of plastic, but we know that they are radically different," Alderman said. "You have to help the kids understand that."

This article was reported by Ruth Mantell for MarketWatch.