There are not too many adhesives that can fill gaps without losing strength. Epoxy is a great product for doing that. It is the perfect product for repairing any loose-fitting joints in the furniture.
* Brush a layer of epoxy onto both parts to be joined
* Assemble and clamp parts if necessary
* Wait for the epoxy to set up
Please do read instructions to determine how long the epoxy should cure before you use the furniture and to reach full strength. If you are repairing a valuable piece, test a small area before.