The saxophone case protects the saxophone while traveling or in storage. Usually, a newly purchased saxophone will also come with a case from the manufacturer made to fit the make and model of the sax.
Within, there is often molded padding and soft material to cradle the saxophone body while in the case along with a small compartment for storing cleaning supplies, neck straps, reeds, and other small accessories. There may also be a small opening for holding the neck piece separate from the body and accessories within the case. Be sure to keep the neck in this opening if you have it, or wrap it in a thick protective cloth or cloth sack if such an opening is not available.
Some cases also have a pair of wheels on one end, which is especially helpful for baritone or bass saxophone players making a long haul.
Cases for Tenor or Alto saxophone may sport shoulder straps or a pair of straps so that the case may be carried much like one carries a messenger bag or backpack. Nylon cases with hard foam, on the other hand, can be a cheaper option for a case purchase. Some cases are also water-resistant, which is nice to know when you are taking your horn about town as it starts to rain. Also, some nylon cases may feel lighter than your standard saxophone case, which can be an added bonus if you are walking with it often.
The most important - yet overlooked - aspect of a Sax case is the owner's tag, which is often attached to the handle of the case. Be sure to fill this out with all of your contact information in case your saxophone is lost to ensure the best chances of retrieval. No a good thing to arrive home after a gig realising you've picked up the wrong horn, just because the cases look the same.
Because saxophones vary in shape, it is best to either purchase a case directly from the manufacturer of your saxophone so that it fits your model, or visit local music shops and try your saxophone in a variety of cases to ensure a snug fit. Poor craftsmanship in a case can result in unspeakable damage to your horn when traveling, so take your time when trying out cases.
If you intend to do considerable traveling with your sax, consider a solid flight case or molded plastic case rather than a soft nylon case. Saxophones are just as prone to being accidentally tossed about on the runway as the rest of the passengers' luggage bags are, so take the extra expense to protect your horn if you plan on international travel. However, some models of solid cases lack an accessories compartment on the inside, so remember to use a separate travel bag for safely storing your mouthpiece, reed, and possibly the neck depending on how the case is designed.
Some of the best manufecturers are SKB, these guys know how to make a great case. Another manufacturer worth trying is BAM Sax Cases.