Depending on what I'm using it for, on wood I use either Tightbond (or something similar), cyanoacrylate (super glue), epoxy, or hot hide glue (the real stuff you mix up from granular form, not the crap from a bottle). Each has it's advantages. Tightbond is strong, drys pretty hard, has a reasonable open time, and is easy to clean up (on a finished surface, use a wet rag - for an unfinished surface, let it skin over, and use a sharp chisel to remove the excess).
Cyanoacrylate is great for small tight cracks that don't need to hold much force, and it's capillary wicking makes it great for tight spaces. It also drys crystal hard.
Epoxy is nice when you need something that will never, EVER come apart, but it make repairs impossible, is incredibly messy, and is very difficult to clean up so I avoid it most of the time. However, if you need to glue steel or carbon fiber to wood, you've got to use it.
Hide glue is the king of wood glues, if you can clamp things up fast enough. It drys crystal hard (noticeably harder than Tightbond, which is a very good thing when you are building guitars), is a breeze to clean up, is very easy to take apart for repairs, and has better resistance to heat than just about anything (when you take it apart, it is actually more the water than the heat that makes it let go. Don't believe me?
CHECK IT OUT.) If it is physically possible for me to clamp something fast enough for hide glue, I do it. It's only real down side is the extremely short open time - as much as 45 seconds. You can stretch that a bit my warming up the pieces you are working on, but you are never going to have much more than a couple minutes. One of these days I'm going to get a video of my dad and our shop manager gluing guitar tops to the bodies with hide glue - it's pretty entertaining. But other than the short open time, nothing works better than hide glue.
Gabriel