Cleaning your saxophone is a necessity. Believe it or not, spit builds up inside the mouthpiece, neck and body. If it is left alone, it will mold and cause problems with the instrument. Fingerprints on the outside of the sax can also create marks and will eventually rust.
There are a variety of tools that may be used to clean the sax. A mouthpiece brush is small and easily slides through the mouthpiece to clean out the spit. You can buy a bottle of sanitizing mouthpiece spray as well. The neck also has a brush that is similar, but longer, and with one side that dries out the inside. The bell must also be cleaned. A cleaning cloth with a string attached is often used. First, drop the string down into the bell, then set the cloth in on top of the string. Flip the sax upside down and the end of the string should fall out the bottom. If you pull this string, the cloth will slide through the body and clean it nicely. Be very careful, though, because it has a tendency to get stuck on key pieces. Lastly, it is a good idea to wipe down the outside of the saxophone to get rid of any fingerprints. This will help prevent marks on the sax.
It is very important that you keep your instrument clean, or it will not work properly. Repairs are also very expensive, so I would recommend that you do your best to prevent damage. You can purchase a variety of cleaning tools on Amazon. Also, Northern Kingdom Music sells cleaning supplies, as does the Bangor Music Store.
picture thanks to http://www.alangregory.co.uk/music/Vincent_Bach_1800B_Mouthpiece_Spray_Cleaner.html