Often, people worry about which trees they should plant if they have clay soil.  One thing that you have to take into consideration is how well the soil drains.  Drainage is the main issue if you are working with clay soil.  If the soil is compacted or water logged, then planting can be very difficult.  If the soil is draining well then you might not have much to worry about.

Many plant and tree varieties are listed as adaptable to soil and moisture conditions, which means that if the soil has more sand or more clay (or if it is fairly moist or fairly dry) then the tree should be able to establish itself.  This doesn't take into consideration extreme cases.  In the case of clay soil, standing water that doesn't soak in for a long period of time would be an example of an extreme case.

One way to check would be to dig a one foot by one foot hole and fill it with water.  If it takes over a half an hour to soak in, then the drainage is slow.  If it takes a half of a day or more to soak in, then the drainage is poor (you may be able to tell this without digging if water puddles up on the soil).  If your soil is poorly draining, there still are some plant and trees that can grow, but you will have to be careful which types to plant.