Most accidents with woodwind instruments happen when they are not encased in between usage periods. Keys can bend out of place and flutes can be really annoying with a banana-like shape.
The safest place
It is recommended, when not in use, to keep the instrument inside the instrument box, as it is the safest place. Equally, damages can be best avoided if not accidentally dropped. It is better to keep them in hard cases rather than gig bags.
Handling the instrument
When playing an instrument, make sure that the position of the hands is applying minimal pressure on the keys. Especially with saxophones, the principal danger occurs with the crook which is the top joint. On the contrary, clarinets have keys that need to be matched from one joint to the next, increasing the risk of damage. All these can be avoided if you are careful enough and learn to handle the instrument properly. If you are in doubt, bring the instrument to a recognised repairer who is expert in brass and woodwind repairs.
Greasing the instrument
Make sure that you grease all the cork joints regularly to avoid any difficulty of playing and therefore, putting unnecessary pressure on the instrument. Some people apply Vaseline as a substitute to woodwind corks, but petroleum jelly is not exactly made to grease and therefore attracts dust, causing more complications to the instrument.
It is true that metal joints on saxophones and flutes need to be greased. But, if the instrument is purchased from a reputed company, there should be no need for lubrication.
Play in clean mouth
A major mistake done by most of the players is, playing the instrument without properly washing the mouth or immediately after having some food. Remember, do not hurry to play immediately after having something. This not only damages the instrument but can also make you feel pukey. It is recommended to play any woodwind instrument only after an hour of having something. This is because, when you blow on something (sometimes with pressure), the esophagus and stomach take pressure and tend to work in an opposite manner. It means that instead of containing the food in stomach, they have a tendency to lift the same upwards. This can cause regurgitation. And when it comes to the instrument, the pads are at maximum risk which may sometimes need to be replaced.
It is recommended to take the woodwind and brass instruments to a qualified repairer at least once in a year for servicing and to keep the instrument in good condition.