What types of trees will grow from a cut branch like a willow tree my grandfather taught me how to take a willow branch put it into water and it would grow roots for planting is there any other type of tree that will do this.

Well... You could start here, propagation newsletter

This link, same site describes the budding process Using the Propagation Technique Known as Budding to Grow Beautiful Ornamental Trees

And for your venerable Willow With apologies to your Grandfather, How to Grow a Willow Tree | eHow.com