Dwarf apple trees are the perfect convenient size for a back yard.
Dwarf apple trees allow you to plant many different apple varieties in a small amount of space. They also produce apples sooner than their full-sized counterparts. Another advantage of these trees is that care is easier since you can reach all parts of the tree. It is easier to inspect for diseases and to spray the tiny trees. Picking fruit is a breeze. If you bag your fruit to protect from pests, there is no problem reaching those fruits. These trees are appropriate for container gardening, so you can have your apple tree right on your patio in a pot. One advantage to a potted apple tree is that you can bring it under a patio roof when it rains and prevent fungi such as apple scab from taking hold on the tree.
The smaller sized trees are achieved by the use of dwarfing root stocks. Most any apple cultivar can be grafted to dwarfing root stocks to make a small apple tree. You just need to be aware of the vigor of the cultivar. The dwarfing root stocks lower the vigor of the tree. Therefore, if you graft a low vigor cultivar onto a very dwarfing rootstock, you may not get much of anything growing. Some common root stocks for dwarfing are listed here.
When you order your miniature apple tree, make sure to confirm the rootstock the tree is on. I ordered a dwarf from a nursery, and when it came, it looked very large. It turned out that they had sent me a standard size tree!