Most plants like soil that drains well after heavy rain. In fact, most of the tags on plants that we buy actually say "needs good drainage," as very few plants can tolerate standing water.
If you have a low lying area in your garden that has continuously soggy soil you may need to consider "bog" plants.
Trees that will flourish in consistently wet soil are swamp maple ( Acer rubrum), which produces small red flowers in early spring; Serviceberry, which has white flowers in early summer; river birch, which has interesting exfoliating bark; and our native Eastern white cedar.
Shrubs that like wet feet are our native spicebush ( Lindera), which has tiny chartreuse blooms in spring; swamp rose ( Rosa palustris); and the red twig dogwood ( Cornus alba), which provides welcome color in the winter landscape.
Perennials that like persistent moisture include:
Siberian Iris
Flag iris
Japanese iris
Obedient plant ( phystostegia)
Canna
Astilbe
Queen of the meadow ( Filipendula ulmaria)
Aruncus dioicus ( goatsbeard)
Ligularia species
Lobelia siphilitica
Cardinal flower, (Lobelia cardinalis)
Meadow rue ( Thalictrum species)
Marsh marigold ( Caltha palustris)
Marsh mallow ( Althaea officinalis)