Glues 
 
Glues have a general ascending order of strength, and the type of surface plays a big role.  Sometimes you want to be able to remove something later, sometimes you want it to hold until the end of time.  Whether or not the glued object(s) move or vibrate in the normal course of operations is important.  It also makes a difference if the glue is acting as a sealant as well as a glue.
Here's the general ascending order of strength: 
 
Rubber Cement — 
 Sometimes you just want to tack something together temporarily.  Rubber cement stays pliable for a long time and rolls right off the surface with your finger when cleaning it up.
   
White Glue — 
 Like the standard Elmer's glue.  Not really very strong.  Good for things that are absorbent, like paper, cardboard and wood, but grows brittle over time and breaks apart with vibration.
   
Wood Glue — 
 Usually cream-colored.  One step above white glue, and works fairly well with wood, but has the same limitations as white glue.
   
Silicone — 
 Actually classified as a 'sealant', it has moderate glue capabilities.  The reason silicone became so popular is that it stays pliable so it's not as subject to stress and vibrations and cracking as 'hard' glues are.
   
Epoxy Caulk — 
 Like silicone sealant, but a much tougher glue.  The stuff they sell at the hardware store is okay, but the real bad boy of this group is 3M's 5200, available at marine stores.
   
Epoxy — 
 In general, I find the ones that take longer to set up do a better job.  There are a number of epoxies out there, so pick the one that suits your surface.
   
Superglue — 
 Superglue likes lots of mating bonding surface, so if you're trying to fill in a bunch of tiny gaps, like with broken porcelain, use an epoxy.  Make sure the surface is thoroughly clean of residue, and Superglue relies on pressure to make a good bond, so hold the project tightly in your hands (or set a heavy weight on it) while it sets up.
 
Like painting, 90% of an effective glue job is surface preparation.  You want it to be absolutely free of any kind of oily residue, and hitting it with a little sandpaper is often recommended.