Premium rewards credit cards also come with personal assistants, or something very close to it. Most issuers offer customer service representatives 24/7 to help cardholders with such mundane tasks as procuring hard-to-get tickets, booking a table at Gordon Ramsay's newest restaurant or coordinating one-of-a-kind travel experiences, such as a cruise with the Food Network, says Thomas Hobbs, director of Discover Network product management, which includes the issuer's Premium and Premium Plus cards.

Other unique customer services include emergency translation services, weather forecasts, ATM locations, referrals for specialty services such as dog groomers and tailors, or locating rare books or other items for purchase.

One Discover Premium Plus cardholder sought help after a tree demolished half his house the night before a big vacation.

"The cardholder called, and the concierge helped track down the cardholder's insurance company and helped them rearrange their upcoming vacation," Hobbs says.

This past holiday season, American Express expanded its concierge services to include holiday shopping for its Platinum cardholders. Those lucky enough to hold the silver card could submit their Christmas (or Hanukkah) lists to the concierge gift-buying service, which would research gift options, compare prices, buy the presents and ship them. The only caveats: The purchases had to go on the Platinum card at a retailer that takes American Express.