Check for annual fees
For a while, this fee was primarily seen attached to credit cards co-branded with an airline's loyalty program, but issuers are beginning to bring it back for more generic cards. For instance, Bank of America has begun assessing a $59 annual fee for some of its credit card holders, the same amount that Capital One charges for its Venture Rewards card. While the fee might be offset by the benefits -- some travel rewards credit cards will reimburse you for checked-bag fees on airlines -- which may make the fee justifiable if you travel often.
Of course, it's easy just to avoid an annual fee when looking for a new credit card by avoiding those cards that charge one. Consider seeking out cards issued by smaller banks or credit unions as well. If a card you've had for a while implements a new annual fee, though, that can be more difficult, but it's worth calling the issuer's customer service department and asking them to waive it for a year.