Size and Age: Peaches and apricots are some of the earliest bearers. A standard size peach or apricot can start producing fruit when it is 3-5 years old. Standard size apple, pear, cherry, apricot and plum trees take a little longer, from 3-5 years.
Dwarf varieties of fruit trees should start producing earlier, many within the 2nd or 3rd growing season after transplanting. But all of these numbers are averages. There are other factors that affect when your tree starts to bear.
Sun Exposure: A tree in full to partial shade is fighting an uphill battle. Fruit trees can survive in partial shade, but they will take longer to begin bearing fruit.
Soil Fertility: Fruit trees, like all plants, require some nutrients to survive. But excessively rich soil or heavy fertilization may encourage branch and leaf growth at the expense of fruit production.
Pruning: All fruit trees benefit from annual pruning, if done in moderation. Pruning rejuvenates fruit trees and encourages the growth of fruiting spurs. Removing more than a third of the tree could have just the opposite effect you were going for and stimulate more branches, as the tree repairs itself, and no fruit. Lack of regular, moderate pruning is one of the most common causes of no fruit production.
In addition to pruning, branches may need to be gently forced into a more open canopy to allow for light and air circulation. This can be accomplished by bending them to as close to horizontal as you can get and securing them with soft rope or twine, staking it to the ground. There are also manufactured "spreaders" that are flexible bars with a 'V' on either end. You can simply position the spreader between two branches to push them apart from each other. Ideally, branches should be in the 10 o'clock and 2 o'clock positions, rather than growing straight up. The old adage is that a bird should be able to fly through your fruit tree without touching a branch.
Frosts & Cold Spells: If buds have been forming and not opening, it is probably the weather that's at fault. A particularly cold, windy winter can damage susceptible flower buds. More likely it would be the result of a late spring frost, especially if the buds have already begun to swell.
Too Much Fruit Set: Too much fruit doesn't seem like it should be a problem, but there are two drawbacks to over abundance. First, a large fruit set means that the trees resources are stressed. You usually have to choose between a large harvest of small fruits or a small harvest of good sized fruits.
Secondly, some fruit tree varieties deal with the stress of a large crop by taking a rest the year after a heavy harvest. They seem to become biennial in fruiting, producing a large crop one year and little to nothing the next.
You can correct both problems by thinning the crop while the fruits are still tiny, about three weeks after bloom time. Remove all but one fruit from each of the spurs or small branch offshoots where the fruit is produced. Leave the largest, hardiest looking fruit to survive. Some fruits will do this on their own. It can be alarming to see fruits falling on the ground, but it is a common phenomenon called June Drop
Pests & Disease: If it's been at least 5 years and you've provided your fruit tree with good care and growing conditions and still nothing, it would be worth calling your local Cooperative Extension office to ask about possible pest or disease problems. There may be a fungus affecting your area or it may be something as large as a deer problem.
It's hard to be patient when you only have one chance a year to set fruit on your trees. But once you get them going, you'll have many, many years of reaping the rewards.