The best glue to use on plastic is JP Weld PlasticWeld, according to Craftech Industries. It bonds virtually every material except Teflon, and the glue spreads to create a gap-free strong bond. It is a two-part epoxy that can be a little messy, and it sets quickly.
Other glues that work well include All Purpose Amazing Goop and Loctite Super Glue. The first can be goopy, so it is not ideal for small projects. The second can cause discoloration or cloudiness, so it's important to be careful in choosing what to apply it to. The worst glue is Testors Plastic Cement. It does not bond the materials, making it useless for any kind of project with plastic.