There is no one glue that will do EVERY job. And, yes folks, that does include Superglue. Just because it can stick your fingers together doesn't mean that it will stick anything and everything!
So which glue to use for what job?
You will want an adhesive that won't soak into your card/paper, wrinkling or distorting it. A solid glue such as Pritt Stick is good for quickly sticking most papers and cards, as is double-sided sticky tape - which can also be used for sticking on flat, lightweight embellishments. Tape is better than glue stick for glossy or metallic card, but is not suitable for mulberry or other fibrous papers.
A thick/tacky PVA glue can used with mulberry paper, but it's best to brush it on for an even application. (Be sure to rinse your brush in water every couple of minutes, to make sure the bristles don't get glued together!)
For “lumpy” embellishments, a thick glue is best for a more secure hold. Good water-based adhesives include Crafter's Pick Ultimate Glue or Tulip Dimensional Paint, both of which are tacky enough to hold the embellishment almost instantly (unless it's heavy) and work on various surfaces so are good for standard, glossy or fibrous card/paper. If these don't work for you, you may like to try solvent glues such as Bostick, Uhu, or Evostick.
For 3D effects, you have the choice of silicone glue (which can take a long time to dry); foam pads (which are very economical but a bit fiddly to work with); or glue dots (which are very convenient but work out more expensive).
When working with translucent paper (e.g. vellum or fine tissue paper), you'll want a glue which won't show through the paper - adhesive spray gives a near invisible finish, and is good for sticking larger areas.
You will probably be working with a variety of non-porous materials and these can be more difficult to stick together. Hypo Cement is good for bonding plastics/acrylics, ceramic, glass and metal, and it has a fine applicator nozzle for precision work.
Ultimate Glue is useful for “floating” or “illusion” necklaces, where the beads are glued onto monofilament.
When glueing on diamante, sequins or other embellishments, you need a glue which won't stain the fabric or dissolve in the wash. If sticking fabric to fabric, it will also be important that the glue dries flexible and doesn't stiffen the fabric. Tulip Dimensional Paint and Hi-Tack Trimit Glue are flexible adhesives which are washable BUT it is best to wash the garment inside-out at a cool temperature, as heat can melt the glue.