Cleaning stuff

Mouthpieces

Immerse the mouthpiece no farther than the beginning of the tenon, in a 1/2 and 1/2 solution of white vinegar, then clean the inside with cotton swabs, paper towels, or whatever. For extremely stubborn depots, you might want to use a mouthpiece brush, but under no circumstances use a brush the has either a metal "handle" or metal bristles.

Cleaning hard rubber mouthpieces, especially older ones, may turn the rubber green, but this has no affect on the sound, response, and so forth. If you can't stand the green, you can polish the outside of the mouthpiece with very very fine polishing compound, but don't touch the mouthpiece bore!

Tone holes

Tone holes should be cleaned periodically with lighter fluid and cotton swabs, but don't soak the swab so that the fluid runs into the bore! 

Don't try to clean tone holes with pads without taking the keys off; getting the fluid on pads may degrade them, especially skin pads. (Luckily, the large tone holes on the lower joint don't often need cleaning, so you won't have to take those keys off.)

Register tube

The register tube should be examined frequently. Any gunk in the tube can seriously effect response, pitch, and sound quality. It's easy to take the register key off and clean the tube with a cotton swab and lighter fluid, but be sparing with the fluid.

Keys

Keys can be cleaned with a dry microfiber cloth and maybe cotton swabs and a little lighter fluid. 

If you want to polish silver- or nickel-plated keys, use a liquid polishing compound and a soft cloth and cotton swabs, not powder permeated polishing cloths. (Powder may get under they keys and maybe gum things up.) 

I don't recommend trying to polish areas that are hard to access because you risk getting polishing compound where it doesn't belong.

Wood

I never use any kind of cleaner on the wood because it's hard to get it in many places and it's rarely necessary. I just use a microfiber cloth.

Some people want to wax the wood to make it pretty, but not only am I not that vain about my instruments' appearance, getting the wax on and off the wood everywhere the wood shows is a pain. 

Tenon corks

The best way to clean tenon corks is to simply just use a cloth. You'd be surprised how clean cork will become with some assiduous rubbing.

Joint sockets

Clean them out every time you finish playing using a dry cloth or paper towel. Whatever you do, though, don't use your swab; you don't want to transfer cork grease and dirt into the bore.