Pentagon Federal Credit Union has a perfect selection of credit cards without annual fee or foreign transaction fee. I use PenFed Platinum Rewards Visa Signature Card, with 5X points cash back for a gas and 3X points cash back for groceries, 1X for other purchases. I have been using this card for a long time, across different states in US and abroad. They also have PenFed Premium Travel Rewards American Express, with 5X points paid back for airfare purchases. I do not have this card, but can recommend it based on others experience. PenFed is a credit union, and you have to join it in order to apply for the card. PenFed offerings have been initially provided to government or military employees only, but as of now everyone can join it through National Military Family Association for example.
Fidelity has an excellent Investment Rewards Visa Card, which return 2% cash back for any purchase. I use it for many years. It used to be American Express, and the only problem with this card was in automatic payments system. However since that time American Express has been converted to Visa and Fidelity transferred its support to other bank, which made this card one of the best (along with their excellent debit card). This card does not have annual fee and charge 1% foreign transaction fee. I highly recommend the cards from Fidelity to everyone, especially if you have international trips.
Citibank also has some very good credit cards, for example Citi Double Cash Card with 2% total cash back for every purchase. I use this card for a while and definitely recommend it for everyone. No annual fee but 3% foreign transaction fee.
Chase Freedom is a famous credit card offered by Chase bank, with generous 5% cash back in rotating categories every 3 months, with no annual fee. While cash back is good, it is difficult to remember those categories. Also they need to be manually activated. For year 2016, Chase Freedom categories included: gas from January to March, grocery stores from April to June, restaurants between July and September, and department stores between October and December. I have this card and use it for some categories like grocery stores, when I can not get 5% cash back anywhere else.
Bank of America has a collection of great credit cards. Although not as great as the cards I mentioned above for general use, they can reward you well in some cases. I use BankAmericard Better Balance Rewards card, with cash back $25 per quarter when you pay at least designated minimum balance each month. Extremely convenient for regular utility payments.