Lake Effect has the good point - different adhesives for different jobs. Start at Jim's recommendation of hot glue - it builds a structure of pretty hard plastic. It fills gaps in rigid joints.
Shoe Goo - it fills gaps and is flexible. It's basically very sticky silicone sealant
Epoxy - Great strength, and whether it fills a gap often depends on whether it has filler in it, the extremes in that direction being Bondo and epoxy sticks.
Model airplane cement - good for rigid connections in plastics.
Gorilla glue - similar in function, and adhere's really well to a variety of surfaces.
Contact cement - paper and fabric
, remains flexible, lower strength than some others.
Wood glue glues wood. Does it well, but not much else.
Super glue - two rigid surfaces that match exactly, such as broken ceramics.
3M 5200. Rigid, no mixing, slow setting, and only removed by burning it off.
So it takes a collection. Each has its role. My collection fills a shoe box, and every once in awhile I take a look and replace stuff that has hardened with age.