Eating glue can have effects that range from relatively harmless to potentially fatal depending on the quantity and kind of glue. Paste and white, water-based craft glues are generally not poisonous, while polyeurethane glues, super glues, epoxies and craft cements all present various hazards.
Contact cement and model cement are both poisonous, and so are some kinds of epoxy. Others offer physical hazards if eaten. Super glues are generally labeled as non-toxic, but if eaten, they can injure the body by fusing the mouth or throat together. Polyeurethane glue expands as it hardens. Inside the gastrointestinal tract, it can form large masses that block the passage of food or even cut and rupture the organ in which it is trapped.
In most cases, glue toxicity is associated with inhaling rather than eating glue. A probable explanation for this is the popularity of using glue fumes as a cheap way to get high. Even glues that are labeled non-toxic can give off dangerous fumes.