If you were to put a speck of heavy clay soil under a microscope what you would see may surprise you. Although clay soil feels like a big lump of heavy soil in your hand, up close it is actually composed of very fine particles that are tightly packed together. Clay soils are generally rich in minerals, but the compaction of the particles makes airflow and drainage a problem. Clay soil should therefore be amended prior to planting. This is good advice for plants with fragile, sensitive root systems. There are, however, plants that will do just fine in a heavy, clay soil. You will need to find plants that have fairly strong and aggressive root systems that don't mind sitting in moisture and that can punch through the clay.
The rose is a lot easier to grow than people think. They will put up with a lot of neglect and still flower for you. Taken care of properly, of course, the rose will have larger blooms and live longer. A heavy clay loam soil is actually considered ideal for roses. Make sure you plant the rose in an area where it will get lots of morning sun and, if it's hot in your area in the summer, it will need shade in the afternoon. Apricot Nectar, a floribunda rose, does particularly well in clay soils.
Day lilies are easy, carefree plants to grow. They need at least six full hours of sun a day to be at their best and will bloom for six to eight weeks in the middle of the summer. The day lily loves water so the moisture content of a clay soil is ideal for them. Allow the soil to dry a bit, though, before watering again.
Often called yarrow, this is a truly low-maintenance perennial flowering plant. They like full sun and an application of fertilizer once per year during the growing season. Achillea can grow to 3 feet in height and may require support. This plant requires water only when the soil becomes very dry, and it will bloom from summer to the first frost.