When is it worth paying an annual fee for a miles and points credit card?

I get numerous emails from Head for Points readers asking for advice on which miles and points credit card they should get. For want of a better way of looking at, assume that your credit card is a book of discount vouchers. Some people take one look at the £300 annual fee on the British Airways American Express Premium Plus credit card and are instantly put off. The American Express Preferred Rewards Gold Credit Card is harder to justify after the free first year. The annual upgrade voucher is identical on the free card and the £240 card – the only difference is that the paid card triggers it at £10,000 of spend and the free card at £20,000 of spend.