Warm vinegar will generally soften the most stubborn old glue on old furniture. Dipping the parts to be reglued in warm water, and then letting them dry out completely, will help to open up the wood pores and allow the new glue to enter the wood more freely. Warming the parts on top of a heater or in the sun will also help open up the pores of the old wood before regluing.
Getting black glue lines on projects? Metal containers like coffee cans can cause this problem, which occurs more often with white glue than with yellow glue. Glues with a pH lower than 7 can absorb iron from the metal, and the dissolved iron can react with certain colored woods to leave black glue lines. Use plastic containers instead.