I’m glad you asked this question. Many casual travelers believe that as long as they limit their carry-on baggage to one suitcase, they’re good to go. Not true. Every ticketed passenger on every domestic airline (with the exception of Spirit, which charges for carry-on bags) is entitled to one piece of luggage and on personal item (such a a purse, diaper bag or laptop bag). However, that piece of luggage must be regulation size. And while there is no industry-wide standard, your carrier will have on its web site the exact dimensions your bag must adhere to in order to avoid being sent back to the check-in counter to pay for a too-big bag.
Helpful hint: In general, if you add the width + length + height of your carry-on luggage and the total number is less than 45 inches, you’re probably good to go.
Here’s a list of links to the carry-on policies for most major airlines: