In addition to making your thumb a lot more comfortable, it will help your hand/finger position by encouraging you to curve your fingers instead of playing "flat-fingered" as many people (shouldn't) do. 

Most of the ones you'll see from retailers are about $10 each. However, one manufacturer sells them on Amazon at two for about $11. This is the description on Amazon:

"2Pcs Yootones Rubber Clarinet Thumb Rest Cushion Protector 1.45-1.75cm"

I've bought these cheaper ones, and they are nearly identical to the more expensive ones that I originally bought from Ridenour Clarinet Products. (Tom Ridenour, the inventor, probably never thought of patenting it and is kicking himself now.)

They fit most metal thumb rests without a problem, but for some, you may have to trim the slot that your metal thumb rest goes into, and if you use a neck strap, trim the rubber to accommodate it. You may also have to remove it when you put your horn in its case.

Using a mouthpiece cushion does four things:

• It opens up your embouchure some, which helps most people's sound.

• It isolates your teeth from the mouthpiece so you don't have as much "bone conduction" so you can get a better idea of what you sound like.

• It protects the mouthpiece, especially if you're a "biter", from making indentations in your mouthpiece.

• It keeps your top teeth from sliding around.

I use several different makes, all from recognized sources such as Vandoren, D'Addario, or BG, because I don't trust the adhesive on cheaper ones. I've had a few of the cheaper ones that variously have had weak adhesive, adhesive that oozes out from under the patch, or adhesive that is a pain to clean off the mouthpiece when replacing them.

Will Robinson! Warning! Warning! (Did I date myself again?) Don't buy the thin ones! They're useless, and do nothing other than protect--for only a little while--the mouthpiece from your teeth. If the manufacturer offers various thicknesses, buy the thickest! (You can even stack them.)

Long ago, before they were manufactured, we old-timers used to cut our patches from tire inner tubes, and some used layers of tape. Both work well, but why bother?

Via con huevos!