Ornamental grasses are great additions to the landscape and will hide the fence for most of the year. Switchgrass (check out Northwind or the shorter Shenandoah) and Karl Foerster feather reed grass will tolerate damp soil.
Turtlehead and the larger Little Joe and Gateway Joe-Pye weed are late summer blooming perennials that will tolerate wet soil.
Arrowwwood viburnum is an upright shrub that produces creamy flowers in spring, blue fruit the birds love, and has good fall color. Red feather arrowwood viburnum has a red edge on the spring foliage that turns green for summer and red in fall. Just more added value.
Before doing any planting, leave enough space between the fence and your plants to allow for their mature size, airflow (this will help with fungal diseases like powdery mildew) and room for maintenance.
So many choices - but hopefully this will give you a few plants to review as you read through our A-Z plant guides.