Overview: Most fruit trees require another fruit tree of the same genus (apple/apple: plum/plum) but of a different variety (Spartan apple/Sweet 16 apple) within about 100 feet that blossoms at the same time for higher yield, larger fruit size, and usually better quality fruit.
Even if they are of the same genus and of a different variety they still may not pollinize each other if they don't bloom at the same time. There are early, middle, and late bloomers, the early and late ones will not pollinize each other but the other combinations will. (Early/early, early/mid, mid/late, late/late)
Beyond genus, variety, and bloom time you may also want to consider restricting your choice to late blooming varieties if you live in an area that habitually experiences late spring frosts. Generally, the order of blooming starts with apricots, then plum, cherry, apple, pear, . . . Apple and pear blossoms are fairly cold tolerant, even late medium frosts don't usually result in significant damage to blossoms, only in the more extreme areas that normally have sudden frosts is it necessary to select for late blooming varieties. (Example: N WI residents who live on a lake have more predictable frosts and very good fruit set, but those in the same vicinity who live in lowland areas away from lakes should keep the blossoming time in mind and be wary of the early bloomers).
However, some fruits have more cold tender flowers, such as peaches and kiwis and others bloom very early, like apricots and some plums; for these, depending on your region and microclimate, choosing the latest blooming varieties may be the most important decision you make in you selection. (See descriptions below under the particular fruit for any unusual blooming habits.)
Other considerations are its bearing habit (whether it bears annually or whether it bears every other year), and also whether or not the variety is even capable of pollinizing other plants. (Those labeled Triploids will not).
If my tables don't mention the bloom time and you wish to try to figure out a tree's bloom time by inferring that it blooms in a certain area at a certain time and want to know when it will bloom in your area, generally the bloom time rating (early, mid, late) shouldn't change from one location to another, relative to other fruits in its class. (In other words if an apple blooms early in Washington state compared to other apples, it should generally be an early bloomer, relative to other apples in Minnesota also)

Note: Unfortunately, unlike ripening times, one can not so easily make such extrapolations regarding absolute bloom times from one region of the country to the other. In other words, you can't conclude: "oh, it blooms in Washington State in Mid May, so therefore it should bloom in central MN about two weeks later." Such predictions might be possible but it would require some indepth research. (as there is the question of dormancy which is determined by weather patterns in the previous fall, winter, and early spring. You would have to figure in the "chill hour" patterns for both locations.)

Pome Fruits

Apple: Most city neighborhoods (and manay rural areas) have other apple or crabapple trees close enough to pollinize your tree to some degree, but it would be best to check to make sure that the bloom times overlap, that the other tree or trees are not the same variety, and that they are not triploids (non pollinizers).

Pear: Pears can be stubborn when it comes to pollinization, their blossoms are low in sugar and less of an attractant to many pollinators (such as bees). Plant at least two, preferably more to hedge your bets, I have no info on pear blossoming times at this time. Also, check the variety description, some aren't good pollinizers.

Stone Fruits

Plum: If you want your Japanese/American plum crosses: Superior, Waneta, Toka, Pembina, etc to bear like you see in pictures with branches bent over from the weight of abundant fruit, then you should plant a native plum nearby such as Prunus americana. Prunus nigra also works. (for more information see: http://www.usask.ca/agriculture/plantsci/dom_fruit/articles/plums.doc)
Plums like to be planted close together, with branches touching, they seem to thrive and bear well this way but traditional planting is fine also.

European Plums: Mount Royal does not require another plum for pollinization but may benefit from another European plum nearby.

Sour Cherries: These do not require another cherry for pollinization.

Cherry Plums: Red Diamond requires a either another cherry plum (Compass has been recommended). or Hansen's Bush Cherry as a pollinizer. (Some have reported that Hansen's Bush cherries vary from one seedling to the next in bloom time and that not all specimens will pollinize Red Diamond but that if you train the Hansen's limbs to be as horizontal as possible they will more likely pollinize the Red Diamond and other cherry/plums). Red Diamond will not produce fruit without a pollinizer.