Sobo Premium Craft and Fabric Glue
Can be used for both paper and fabric, but primarily is used for paper and is essentially a standard, all-purpose white glue. It's safe for children to use as well.
Great fabric glue that can also be used for lace, leather, and trim. This glue is not child-friendly.
Original Tacky Glue from Duncan Crafts
Sticks immediately, but is not quick-drying, which is great when you're working on a vertical surface and you're afraid that whatever you are gluing will fall. It is also child-friendly.
Elmer's Wood Glue
Needs to be clamped down while drying to be effective, but once the clamp is removed, you'll have a good seal.
Bond Multipurpose Cement
Powerful, long lasting, and has a very loyal following among crafters. This is more powerful than the other glues and should not be used by children, because it is toxic.
Our last one is the glue gun, a favorite of many crafters for its versatility. Be very careful using this -- if you get any on your fingers, your first instinct will be to pull it off, which will cause you to burn the fingers on your other hand when you try to pull it off. Martha likes to keep a bowl of ice water next to her so if she happens to burn herself, she can quickly immerse her fingers into the bowl, and the glue congeals, allowing it to be peeled off without burning. Glue guns should not be used by children -- only by older children and always with adult supervision.
All of these types of glue can be found at your local crafts store.