Trashman,
Go to home Depot and buy DAP Weldwood glue. It's designed for wood and it's one of the best on the market. Never use white or Super glue. Gorilla glue is not that good either.
Gorilla Glue is actually fantastic glue, especially for outdoor use. It is waterproof and performs well at all different temperatures and through wild extremes of temperature and humidity. (Boat builders glue (resourcinol ?sp?) is also a good choice in these conditions.) Also, Gorilla Glue (which is polyurethane glue, and can be bought cheaper in "generic" form) is superior for gluing end grain against regular grain. That is if you butt up the end of a board against the flat of another board, Gorilla Glue is better than Titebond or Aliaphatic Resin, etc.
And white glue is nearly as strong as wood glue, IF you clamp the joint properly.
As I said before, most of these glues are way strong enough. The whole "this glue is stronger than that" thing is more of a marketing gimmick than anything else. A lot of other considerations are more important than ultimate glue joint strength. Heck, as long as it's stronger than the wood itself, it really doesn't matter all that much.
Considerations like clamp time, water-resistance, whether or not you'll ever need to take the joint apart, the materials to be glued, whether or not you'll be able to clamp the joint, toxicity, fumes, ease of use, color, what contaminants are already in the joint, and so on, are probably all at least as important as glue strength.
For example, I found Gorilla Glue worked nearly as well as epoxy for joints on piano benches (they always take a beating!) that were hopelessly mucked up with white glue. Also Gorilla Glue works great on stone or ceramic or clay (providing the surfaces aren't painted or glazed), plus it foams up to fill gaps and spaces--not as well as expoxy, but still, to a degree. And it's nicer to deal with than epoxy. If some excess spills out of the joint, you just wait for 10 minutes or so until it is sort of dry, but still somewhat soft, and you can trim it right off with a chisel. Epoxy on the other hand--ESPECIALLY epoxy that hasn't been mixed right, is a royal, royal pain in the rear end when it gets on surfaces or on your hands. I HATE epoxy hardener or resin all by itself. Nasty. Yuck! But Gorilla Glue, while it does stain your hands, isn't nearly so nasty to deal with.
There are pros and cons to the various glues; that's for sure.
And then, of course, a lot of times what you really want to fix a joint or connection is a
SCREW!!! Or both. That's good, too.