I have travelled with my ukulele. And some airlines has clearly stated in their website about the baggage information. Mine is a soprano with hard case, I always take it as a carry-on baggage, and put it under the seat or in the overhead compartment.
Take United Airline as an example:
http://www.united.com/web/en-US/content/travel/baggage/fragile.aspx
"Musical instruments
Musical instruments can be carried on board or checked as baggage. If necessary, a seat can also be purchased for an instrument.
Carried on board
A small musical instrument can be carried on as a personal item. If the musical instrument appears too large or irregularly shaped to fit under the seat or in the overhead compartment, it will not be accepted for in cabin stowage.
Checked as baggage
Instrument should be in a hard shell case to protect it during normal handling.
Excess charges apply if checking more than the baggage allowance.
Oversize charges apply to musical instruments that measure 90 - 115 linear inches.
Overweight charges apply to musical instruments that are over 50 pounds.
Musical instruments over 70 pounds will not be accepted.
If the instrument is over 115 linear inches, contact United Reservations.
In addition to the above polices, stringed instruments should have the strings loosened to protect the neck from damage due to expansion and contraction which result from temperature variations.
Cabin-seat baggage
United will allow a customer to purchase a ticket for a musical instrument which is too fragile or bulky to be handled as checked baggage. Upright basses and guitars will not be accepted as cabin-seat baggage.
Excess Valuation may not be purchased for musical instruments."