If you have followed my advice you already have great travel credit cards when arming your wallets with the best Hotel Credit Cards like the Hilton Amex or the Marriott Chase Card! The Amex Platinum Card is the best travel card due to its benefits for both airlines and hotels.
If the Amex Platinum Card high annual fee is not for you, and you are loyal to an airline, consider getting an airline branded credit card. All of the major airlines like Southwest, United, Delta, and American Airlines all have branded credit cards. Those cards don't typically offer a lot of earning potential but they do come with sign up bonuses which get you well on your way to free travel. The Delta Amex
They typically only give you 2-3 points per dollar where as the Amex Platinum gives you 5 points per dollar.
Southwest Chase Card is a good card to get. Hold out on getting this card until they offer a sign up bonus to help you get the Companion Pass. The Southwest Companion pass is one of the best airline reward programs which can yield tons of free travel. To qualify you need to earn 125,000 points or fly 100 one way flights. I got this card 2-3 years ago and got two years of Companion Pass which allowed me to essentially travel for 50% off. You can change your companion up to 3 times a year. This is a HUGE benefit as we are able to take 10+ flights including multiple trips to Hawaii and across the country.
The Delta Sky Miles Reserve Amex is a pretty good card if you are loyal to Delta. It even includes a buy one get one free flight that is even good for First Class! They won't let you fly to Hawaii but if you do any East Coast to West Coast travel this is a HUGE benefit especially if you can score two first class tickets on there lie flat Delta One seats.
American Airlines doesn't really have a good card to help you earn a lot of miles (only offer 2x on airfare purchases) but some of there cards come with Admiral Lounge Access and medium sized sign up bonuses. They recently restructured their status to make it more favorable for using their credit card. You could earn status and get upgrades to premium seats by spending a lot of money on the card. Of course, its not guaranteed but if you do a lot of flying on American Airlines it could be a valuable perk.
Alaska Airlines still is one of my favorite travel credit cards. If you don't live on the West Coast it isn't the best card to have as most of their routes are on the West Coast with the exception of Newark, New York, Florida, and Boston. The low annual fee makes it an easy card to hold as it comes with a companion pass (just pay for the taxes and fee) plus an annual Alaska's Famous Companion Fare that lets your second traveler fly for only $99). This is a huge benefit when flying during peak times like holidays or long flights to Hawaii or Alaska. Additionally, Alaska has one of the most favorable transfer award partners which I have used to score some of my favorite flights (Qantas First Class, Qatar Q Suites, etc)
However, If you are looking to score some of the best seats in the world, the Amex Platinum points allows you to transfer to multiple airlines and even hotels giving you the most flexibility. Being able to transfer points to programs like Qantas, Emirates, or Singapore Airlines is a huge benefit as you most likely would never earn points on those airlines.
Pro Tip: Keep a look out for Amex transfer bonuses throughout the year. Right now, Amex is currently offering bonuses on Virgin, Qantas, Hawaiian Airlines, British Airways, etc.