Everything @Sgtmajormummy said plus cashback (or cashlike points, eg John Lewis, Amazon, a supermarket etc), plus a good way of simplifying budgeting and managing cashflow.
If you have a mortgage, most people take a fixed rate that they need to renew every so often, so keeps your credit history good to get the best rate.
Unless you have so much spare money you could always buy a new washing machine, car insurance boiler etc without going into overdraft - use of credit card and pay off every month - good, use of overdraft to pay for this expense until payday - bad, in the banks eyes, and can be expensive. Even if your overdraft doesn't cost you anything, the banks see it as bad to use it, makes little sense, but there you go, play the game.
If there's a problem with your DHs credit card (system goes down, lost, stolen or hacked) you have a back up.
So I'd agree that you should have your own credit card. I suppose another reason would be, the what ifs. What if your DH died or you got divorced. You wouldn't want to deal with the downside of a thin credit file when you need to be getting your own mortgage etc based on your history alone.
What I don't understand is the people who put all their money in one current account and pay all their bills and spending out of it.
Unless you keep a lot of spare money in there, you have to watch it closely to make sure you don't spend bills money on groceries, fuel and general spending.
If the system goes down, or you lose the card, you have no easy means of accessing your money until it is sorted.
How do you buy a gift for your partner without spoiling the surprise?
So unless you're one of the people who see a credit card as free money waiting to be spent instead of a useful payment tool, yes, you do need one.