Recently Guitar Player Magazine posted a misleading article that, in the United States, airlines are required by law to accept your guitar as a carry-on. read it here
While it's true they will sometimes let you on with your small guitar or instrument, be careful. If its a full flight without much space you will have to check it. Even with the best case scenario of a gentle and careful baggage handler, the temperature and pressure changes in the hold are not good on your instruments.
The use of the language "required by law" is very misleading. That only means that it can exceed the usual dimensions allowable for a carry on. If a flight attendant or gate worker tells you that you have to check one of your carry-ons — any of your carry-ons — then you do what they say or you don't board.
If you must fly with your guitar, try to bring it as a carry-on but use a good hard case as a precaution. Make sure not to exceed the carry-on limit; your instrument does count. If there is no room for it in the overhead, politely ask if there's a closet somewhere you can stow it. If they still say no, check it at the gate like you would a stroller. Never check your guitar or instrument at the ticket counter.
Another option is renting a guitar. Here at Kauai Music and Sound, we rent guitars to travelers on a regular basis. We rent by the week and it saves traveling musicians so much hassle and risk of bringing their own instrument. Check local music stores in the area you're traveling to to see if you can rent a guitar.