Re: RE-covering formica kitchen cabinets
If you want to do a full reface on them, including new doors, then you need to see if the faceframes are up to the task. See how well they are holding the hinges/screws. If all is tight, you have acceptable boxes for a reface.
there's really no way to reface the laminate doors (melamine over p-board most likely) and a more respectable door style will actually give you a tangible result, any less will look only like a paint job. There are many places that manufacture cabinet doors for the refacing industry; find one nearby because doors are heavy and the shipping can kill the budget. Find a door you like in a finish you like, and you're off to a good start.
If the cabinet boxes are frameless, then there is really nothing worth saving, as you have nothing but particle board there to fasten to. In that case, paint away.
Remove not the ancient landmark, which your fathers have set.