I’ve been looking into this credit card. It’s offered by Chase, and offers some great rewards. You get triple points at Amazon, double points at restaurants, drugstores and gas stations, and regular points (1 for $1) elsewhere.
They offer gift cards, cashback and travel opportunities. (For the travel, they offer hotels, rental cars, round-trip airline tickets, money off an airline ticket, and points/miles for a specific airline. 5000 points—6000 British Airways miles.)
Obviously, though, this card would be best suited for someone who uses Amazon a lot. (I do.)
I think @willbrawn‘s card sounds like the best bet, if you have a Southwest near you, and you’re not interested in anything but airline miles.
Also, if you have a preferred airline, you might try checking their home page or affiliates—they might offer a credit card that does exactly what you’re asking for.