To bond plastic to plastic, the best types of glue are epoxy glue, such as J-B Weld's Plastic Weld, or super glue, such as Loctite Super Glue. You can also use hot melt glue sticks, depending on the plastic type. Plastic cement is not effective at gluing plastics.
Don't use super glue on acrylics since it causes discoloration and is difficult to remove. It works well for gluing other plastics, except for gluing Teflon, thermoplastic polyurethane and nylon plastics together. Epoxy glues work well, but are messy and set very quickly. Hot melt glue sticks are effective for gluing nylon but vary in effectiveness for gluing together Teflon, polypropylene, thermoplastic polyurethane and polyvinyl chloride.