Adhesives

Animal glue, Gelatine glue: Traditional theatrical glue
Softened with water and melted in glue pot or double boiler.
Strong, but messy to make and use, Rots quickly.

Wheat Paste:
Flour and rat poison.  Used to glue muslin to flat frames.
Replaced by White glue.

White glue (Elmer's White Glue, etc.):
Polyvinyl Acetate glue.  General purpose adhesive for porous surfaces.

Yellow glue, Carpenter's glue:
Specially formulated for use with wood, less suitable for other materials.

Flex Glue, Flex Bond:
Also polyvinyl acetate, but formulated to be flexible when dry.
Less strong than White glue, but sticks to more things.

Construction Adhesive:
Thick caulk-like adhesive, comes in tubes for caulking guns.
Very strong, fills voids, can be a bit messy.
Available in variety of formulations, for wood-to-wood, wood to metal, 
foam board, etc.
Trade names: Liquid Nails, PL200, PL 300 (foam), etc.

"Hot Melt" Glue:
Rubber based polymer, melts at low temp and sets when cool.
Not very strong, but sticks in seconds.

Epoxy Adhesive:
Two-part setting polymer, forms solid resin when set.
Very strong, sticks to most materials, fills gaps well.
Available from "quick setting" to "slow setting".

Contact Cement:
Sticks instantly when dried coatings come into contact.
Very strong, but cannot be separated and repositioned.

Urethane glue:
Fairly recent wood glue, sets from reaction with moisture.
Very strong, with some flexibility when dry.
Some gap filling ability.