3. To influence the growing characteristics of the desireable variety.
Grafting can be done, with success, within a species family: i.e., apples - crabb, red, yellow, bicolor, etc.; stone fruit -peaches (either early or late ripening), apricots, plums, cherries. It cannot be done with 2 different species; such as, an apple to a pear, or a peach to an apple. But peaches can be grafted to nectarines, plums, and sometimes cherries or vice-versa. The closer to the species "normal" traits, the better. An apricot variety may be grafted to a peach or plum tree, but with cherries the success rate declines; whereas, a plum can be grafted to cherry rootstock, other plums and to apricot trees. I think you get the idea.
We graft to change the already growing and established variety. In Washington State, May apple orchards, planted and established as "Red Delicious" apples, have been grafted by more desireable varieties. Such as, Fuji or Gala. Where the return, 1 acre of Red Delicious is declinging, the return, 1 acre for Fuji, Gala, Braeburn, has been increasing. Since the tree has already established itself, rather than pull it out to replant a "newer" variety, they simply cut off the major branches, back to stubs, and graft the newer variety on to the stubs. Production is back within 2 years, with a lot less cost and labor of replanting involved.
Sometimes in an orchard, damage is done to a well established tree that threatens to kill it, if left untreated. Girdling (the removal of outer bark and cambium layer) occurs from rodents or mechanical damage from the normal orchard tilling or mowing. By taking small twigs from the upper part of the tree, and cutting the ends of each twig at steep angles - to expose the cambium layer - you can graft below and above the damaged area. This is known as bridge grafting. It literally establishes a bridge from the lower part, across the damaged area, to the upper part of the trunk; to allow nutrients to again flow both ways, thus saving the tree.
The third main reason for grafting is to influence the upper part (scion) of a variety by the characteristics of the lower part; in the ground - ROOTSTOCK. Dwarf apple trees of any variety are grafts between the variety of one and the dwarfing chracteristics of the rootstock. Some rootstock induce more dwarfing charcteristics than others; better winer hardiness or earlier maturity of fruit. Rootstocks can even affect the size of the fruit grown above it. Most apples are larger on dwarf rootstock; i.e., M26, M9, Bud9, P2, Mark, than on a full size tree rootstock. Rootstock never affects the color or taste of the fruit. In fact, on one given apple tree, as many different varieties can be grown, as there are branches or twigs available, and would still be affected by the rootstock only in growth habits and size of fruit.
Grafting is a lot of fun and adventure. Seeing one bud grow into that variety is amazing. It is limited by only the imagination of the grafter.
Suggested Reading Material
The Grafter's Handbook by:R.J. Garner ISBN:0-304-34274-2