There are 2 different topics to cover when discussing care and cleaning of your saxophone. The first is mechanical and the second is cosmetic. Mechanical care covers the things you can do to keep your saxophones in top working condition. Cosmetic cleaning has more to do with keeping your instruments looking great.
Let's look first at the mechanical care and cleaning. I think the most important area and greatest cause of problems with a saxophone comes from not being careful with your instrument. This list can include sitting on your case, throwing it in the car, leaving your sax on a sax stand where it can be knocked off, shoulder straps twisting causing the sax case to fall off your back, not hooking the neck strap on and dropping the sax, dropping a mouthpiece or neck during assembly, forgetting it is on the chair or bed and sitting on it... You get the idea. Caring for your saxophone starts with respect for the instrument and being careful both inside and outside of the case.
The saxophone has many moving parts that have a specific adjustment relationship to many other moving parts. When any of these are banged up, the result can be a needed repair. If you treat your instrument with respect and exercise care in handling, you will be blessed with a sax that works great.
Since your breath has moisture, the inside of the sax is always getting wet. Saxophone pads are made from a couple of different materials that can end up getting damp also. It is very important to clean the inside of your sax with a swab, pad saver type devise or both. I use swabs for the sax body, neck and mouthpiece. I also use a pad guard after I swabbed the sax body and leave it in the body until the next use. If you only want to do one of these, I think the swab is the better to use. To those that already have pad savers: swab the sax and then leave it out to dry a little. Just shoving in a fluffy stick can keep moisture against the pad and not really help much in drying pads quicker. Replacing all swabs and pad savers every 2 years is a very good idea for smell and bacteria problems unless you can safely wash them with hot water.
The benefits to cleaning the inside of the sax are many. The pads will last much longer, and it reduces any smell and risk of health issues caused by spit, bacteria and food particles resting in the sax, neck and mouthpiece for long periods of time.
Funny story - I was in Oklahoma City and needed a repairman. I was brought to this guy named Dooley, who told me stories as he fixed my sax. It seems Charlie Parker used him when in town, and one day showed up at his door and said, "Dooley, my sax won't play!" Dooley stuck a light down the bell and it stopped at the bowl. He grabbed a flashlight and looked down the bell and saw it was stopped up with old food! I guess Parker had been eating on the gig and it added up to a big mess.
Regular maintenance is easy if you just get in the habit of cleaning the spit out after every use.
I know many of you love your sax and want to keep it looking great! Many of us have a high level of acid in our fingertips that will eat away lacquer really fast. If you take the time to wipe your sax off, you can extend the life of the finish and keep it looking like new. Soft micro fiber cloths are best and you should have one in your case so it can be used often. My only caution is: watch what you are doing while cleaning. You could pop a spring off or bend a key if you are not careful. Basic care and cleaning is a lifestyle and with regular care and cleaning, your saxophone will perform better.