When choosing a bike bag / box you will have to make a decision between added protection or increased luggage weight. A solid bike box will offer the ultimate protection to your bike but will add many kilos to the total of your luggage (see booking your flight). A canvas bag or cardboard box will be many kilos lighter but your bike will not be so adequately protected from the sometimes, not so careful, handling of the baggage handlers.
Many problems can be avoided by careful packaging of your bike before placing it in the bag. Remove any parts that could be snapped/ bent (ie rear mech, brake levers etc). Use some pipe lagging / bubble wrap to protect your frame and other parts that might be exposed to damage from luggage being placed on top of your bike back or from unscrupulous and inconsiderate handling.
Check your bag / box and if necessary, bike on arrival and report any damages immediately to the airline.
No need for undue worry, the Yak Attack team have travelled extensively with their bikes over the last 10years, just using a normal canvas bike bag and have (so far) never encountered any damage.