Sure. Your success will depend on the type of tree you are transplanting, its size, and how well you protect the root system while digging and transporting the tree to its new location.
Trees with a tap root (oaks, hickories, pines) will not transplant as well as those with a fibrous root system. When digging, make sure you get a large root ball, so as to get as much of the root system as possible. Wrap the roots and attached soil in wet burlap or plastic, keeping the trees moist and shaded while transporting and preparing your new planting hole.
Dig an adequate hole. Planting holes should be twice as wide and as deep as the root system of your transplant. Place the tree in the hole and backfill with soil, taking care to keep out any sticks or rocks. Firm the soil around the tree with your hands. Do not use your foot - this compacts the soil too firmly and is commonly referred to as "the death stomp."
