Depending on your type of model there are a number of choices when it comes to gluing a model. All are available at a local hobby shop.

Wooden model
Professional wood glue works best for wood, Franklin or Elmer's brand. These types works especially good for wood that has been wetted to allow for bending. A builder can also use thicker grades of CA glue or Epoxy. 

Plastic models, wood and R/C

Cyanoacrylate or CA glue is the choice for builders when assembling deck parts and details. The glue comes in three different grades of thickness. How thick of a grade to use depends on what you are gluing. 

• Thin CA is used for most initial assembly and tack gluing. It dries in a few seconds.

• CA+ (Medium gap filling) is used for surface gluing, filling small gaps between parts and general purpose applications. It cures slower in about 20 - 30 seconds.

• Thick CA can be used when extra positioning time is needed. The thick type works well as a gap filler and is also used when a little extra strength is required. 
  *The glue puts off strong fumes when curing, work in a well ventilated area

Epoxy
Epoxy is used when the joint requires exceptional strength, such as when installing engine mounts, shafts, or other parts that will vibrate or become wet. You mix equal parts of resin and hardener, stir well, then apply a thin film to each part and clamp. 

• 5-Minute epoxy is used for simple, small gluing operations where elaborate alignment is not required. Working time is about 5 minutes, handling time 15 minutes, and it's fully cured in about 1 hour.

• 30 - 60+ minute epoxy is used for extra strength (because it can penetrate longer) and where several parts must be aligned and checked before it cures.

(Don't use extra hardener in the hopes of making the mixture harder or work faster. Just about all epoxies work best with exactly a 50/50 mix. When you increase the amount of hardener you run the risk of causing the cured epoxy to become either brittle or rubbery -- neither being as strong as a properly mixed batch.)