Today I found my computer headset under the wheel of my office chair. It was broken. Since it is plastic it is usually not very easy to fix with glue. Some super glues might be able to bond, if it likes the plastic.
The solution today was to use Polycaprolactone (PCL), a non-toxic polyester thermoplastic. It melts when put in hot (boiling) water and then you are able to shape it with your hands. Be careful not to burn your fingers. When it cools of it is very similar to nylon, strong with a bit of flex. Also, it is reusable, just reheat it, and you are ready to get to work. People also use it for molding plastic parts.
The result was maybe not very beautiful, but at least I do not need to buy a new pair.
The shapable plastic can be bought from Ebay or other stores. It is not very expensive. Search for InstaMorph, Polymorph or Moldable Plastic.
Some more detailed information can be found at http://www.robotroom.com/Prototype-Plastic.html and http://dlnmh9ip6v2uc.cloudfront.net/datasheets/Prototyping/Make_With_Polymorph.pdf
Good luck with your repairs and projects!