White Glue (PVA Adhesive)
This is a very simple and common glue; we all probably recall Elmer's glue from our schooldays. It's safe, easy to use, and inexpensive. It does lack a high bond strength and can be unsightly, so select it for applications where the glue will be hidden and not put under a lot of strain (e.g. trims, detail lines).
Liquid Latex
Yes, it's possible to apply liquid latex as a glue. It forms a good bond with latex and porous materials; this is probably the best way to attach individual hairs to a mask. Latex can be pre-colored by mixing it with dyes. It doesn't have great bonding strength and it will break down over time, so don't use it for anything critical or long-term.
Silicone Glues
These are more special-purpose glues, designed to form semi-flexible waterproof seals. Silicones are generally available in tubes and may be applied directly and then smoothed with an applicator. (A lot of caulking is silicone-based, but we're not including that since it doesn't have a strong adhesion to it.) Silicone glues take a while to fully dry, but can sometimes be useful for bonding troublesome materials.
PVC Cement
They sell small cans of specialized glues that plumbers use to seal joints in PVC piping. While I can attest that it does a good job of holding pipes inside couplings, I've never tried to use this adhesive for any other purpose. If anyone out there has, please let me know how it went. (By the way, this stuff is kinda nasty; be sure to read the safety precautions.)
Duct Tape
Okay, okay, so it's not really a type of glue... But duct tape is so useful that I couldn't ignore it! Keep some with you for emergency repairs. For out-of-sight parts of the costume, duct tape is often the fastest and simplest way to keep two pieces of whatever stuck together. If you have access to gaffers' tape (often used for theater work), that's even better.
