If your glue joints have a tendency to fall apart, don't blame the glue. You must be doing something wrong, because modern woodworking glue will produce joints that are actually stronger than the wood itself. All you have to do is use the glue properly.
Make sure the joint fits together well. No glue will give much strength if the parts being glued are rough, warped or poorly cut. These keep the parts from fitting snugly.
Make sure the wood is clean. Glues rely on penetration to achieve full strength, but wax, dirt, grease, even natural resins in the wood can interfere with penetration. Wipe parts to be joined with a rag dampened with a strong solvent, such as lacquer thinner.
Avoid end-grain joints when possible. End grain is naturally weak, and it soaks up glue like a sponge, drawing it deep into the wood and out of the joint. The result is a dry, weak bond. If you can't avoid and end-grain joint, reinforce the joint with cleats, nails, screws or dowels. Or use special joints that interlock to add strength. And to overcome the problem of the dry joint, "prime" the end grain before gluing - thin the glue (use water for white glue or yellow carpenter's glue) about 50 percent. Apply a coat of this thinned glue to the end grain and let it soak in for half an hour. Then apply full-strength glue and assemble the joint.
Keep the parts immobile and in firm contact while the glue sets. Clamps are the neatest approach since they don't show as nails and screws do. But don't overtighten them and squeeze all the glue out of the joint, producing a "starved" bond. Tighten the clamp just enough to bring the parts into firm contact. To keep the clamps from marring the wood, pad the jaws with scraps of soft wood, or pieces of carpet.
Use the right glue. For general interior work that won't be exposed to moisture or unusual heat you can't do any better than white or yellow glues . . . the stuff sold in squeeze bottles. For wood joints that will be exposed to the weather, use resorcinol glue. Joints that must be dishwasher safe (on knife handles and the like) need epoxy.