If your project requires joining two pieces of plastic and need a stronger connection than you'd get with glue you can weld two pieces of plastic together by using a rotary tool to spin a plastic rod. The friction from the rotating rod placed against the plastic will form a weld.
Engineer Fran Blanche's weblog describes how she recreated the 1970s Mattel Spinwelder toy from her youth using an inexpensive rotary tool holding plastic welding rods. The technique doesn't make for a particularly attractive weld but as evidenced by the above video it should be quite sturdy for most applications.
Most plastic welding kits seem to use a specialized tool that looks like the child of a soldering iron and a hot glue gun that ranges from $30-150. It's nice to know that friction welding works well.
Ask Fran: Build Your Own Friction Welder | Fran's Writings on Design and Engineering