Two cards received honorable mention status, with one nomination each. Hardekopf nominated Gold Delta SkyMiles from American Express, which offers 30,000 bonus miles if you spend $500 in the first three months. You earn two miles for every purchase on Delta or for a supermarket or gas station, and one mile for everything else. The $95 annual fee is waived the first year, and your first bag is checked free.

For auto travel, Papadimitriou likes the PenFed Platinum Rewards Card, which he called "the best gas rewards credit card on the market." The card offers five points per $1 spent on gas, three points per $1 at supermarkets, and one point per $1 on everything else. The card also gives $250 in initial bonuses when you spend at least $1,000 during the first three months.

Cash back

Capital One takes top honors in this category, too. Four experts nominated the Capital One Cash Rewards, a no-annual-fee card with a "very simple and straightforward reward structure," as Woolsey put it. The card offers a $100 initial bonus for spending $500 in the first three months, a 1% rebate on all purchases and a 50% annual bonus on all the rewards earned each year.

"This card is great for people who don't want to be bothered with keeping track of how much cash back they earn in a certain spending category, when they have to sign up for bonus categories, etc.," Papadimitriou said.

A longtime favorite once again made the list: American Express Blue Cash Preferred, nominated by three experts. "The Blue Cash Preferred gives unlimited, high rewards rates on the purchases people make most: 6% cash back on groceries, 3% on gas and department store spending, and 1% elsewhere," Sekar said. "It has no spending thresholds or caps, and its $75 annual fee is mitigated by the current $150 sign-up bonus and by the spectacular rewards rate."

Stubbs agreed that the annual fee "will pay for itself very quickly if you use the card on even a semi-regular basis." Those who want to avoid annual fees can consider the version with a less robust rewards program, the American Express Blue Cash Everyday Card, she said.

Chase Freedom is NerdWallet's favorite no-fee cash back card, Sekar said, and Hardekopf liked it as well. "The Freedom offers 5% back on rotating bonus categories that change quarterly, up to $1,500 spent per quarter, and an unlimited 1% back elsewhere," Sekar said. "The categories are broad, helpful and seasonally timed. For the summer driving season, it currently gives 5% back on gas and restaurants."

Honorable mentions: Citi ThankYou Preferred Rewards Visa, which Woolsey liked because its "excellent online merchant network offers special discounts and extra point-earning potential." The no-annual-fee card provides 15,000 ThankYou points for spending $1,000 in the first three months, which can be redeemed for $150 in gift cards or cash.

TrueEarnings Card from American Express, another Woolsey pick, "makes the most sense for Costco members but offers strong cash-back purchase category incentives on gasoline (3%) and restaurants (2%) along with 1% cash back on all other purchases. No annual fee for Costco members."

Papadimitriou singled out U.S. Bank Cash+ Visa Signature Card, which "allows you to tailor your rewards to your biggest expenses and does not charge an annual fee," he said. "You earn 5% cash back on two spending categories of your choosing; 2% cash back on gas, groceries or drugstores; and 1% cash back on everything else."