Q. Are there any airline companies that do not charge for luggage besides Southwest?

A. Southwest doesn't charge for the first or second bags, unless they're oversized or overweight. JetBlue also doesn't charge for the first checked bag, and neither does Air Canada or most other airlines flying internationally from the U.S. 

All other domestic U.S. airlines charge for checked bags, and as you may have heard, starting Aug. 1 Spirit Airlines will begin charging for any carry-on luggage that doesn't fit under the seat in front of you.