Adhesives?

Depending on how small the part is, try some ordinary super glue. For bigger stuff and stuff that sees more stress, there is an epoxy by west systems that works fantastic. It's pretty expensive and it's a two part system. If that sounds like too much work, try the five minute epoxy that any hardware store will have.

you really should try to determine "what" type of Plastic it is that you want to repair. I would use "Loctite" they make many different adhesives for what you are looking for.
Some epoxies will "NOT" work on plastic. The west system that S7horton mentioned, I have not used but know of others that have and they claim great results. And yes, it is expensive.

Please excuse my ignorance, but how does one determine what kind of plastic one has? Any thougts on adhesives for metal?

a lot of the "OLD" type knobs were made of Bakelite. New knobs are molded in: Styrene,lexan which is Polycarbonate, acrylic,butyrate and other various plastics. Without seeing I cannot advise on the plastic in question.What part of the country are you in ? I might be able to direct you to someone. Metal to Metal "LOCTITE" for sure. If you go to a Home Depot, Lowes, Hardware Store and just ask them which Loctite they would recommend. It is a ONE componet adhesive.
Graingers is another source.
I have not used it but you can go on line to Loctite and check out all the various adhesives.
If you like e-mail me with other questions on your projects and if I can help you I will. I have been in the "PLASTIC"
Industry for over 35 years.