"Veneer adhesives usually can be broken with heated white vinegar. It's a smelly process, but it works. The trick is getting the first edge up to get teh vinegar to where the glue is. I usually use a chisel or sharp utility knife.
The veneer can be replaced with veneer, or a laminate such as formica.
There is a possibility the wood underneath will look good enough to just leave it is as - but I wouldn't count on it."
"My mother refinishes antiques, this is how she told me to remove vaneer. you will need an old bath towel and an iron with steam. but the bathtowel in how water, squeeze lightly, place on vaneer and apply hot steam iron on the towel and continuously press the steam button, this will melt the glue underneath the vaneer allowing it to come off. Be patient and lift off slowly."
"I'ved used the same method, but I don't set the iron on steam. The steam generated by the hot iron on the wet towel is usually enough.
PS - this method works well IF the piece is stripped of all finish.
PPS - this is also an excellent method to remove dents in softer woods. Again, it works on RAW wood - not through a finish "