Superglue works well for glass and metal parts, but when repairing plastic use Loctite or JB Weld PlasticWeld. It's important to note that most superglue formulations contain chemicals that melt plastic, which can cause the adhesion to fail in addition to creating potentially dangerous fumes.
Loctite is a brand of epoxy glue popular for plastics, but other types of epoxy work as well. However, epoxy often must be used in two steps, and the adhesion it creates is difficult to break. Epoxy glue is a great option for attaching different types of material. JB Weld PlasticWeld is designed to glue plastic to other plastic, but it can also glue plastic to metal or glass.