The ericaceous plants are not good if you have a continuously wet soil, they will get root rot. If you can provide a light humousy soil that is constantly moist but not saturated, that would be OK. Dogwoods? Astilbe (some are OK in shade, many are not)? Hostas? I guess a lot depends whether the wet soil is a clay pit or not. Winter Jasmine seems able to grow anywhere. Ferns would seem an obvious choice, but look for those that specifically like wet feet because some don't. Try Iris pseudacorus if it isn't too dark.

Acer, Aconitum, Alchemila, Alliums, Arum lilies, Aruncus, Arundinaria, Astilbe, Azalea, Berberis, Bergenia, Brunnera, Carex pendula, Chamaecyparis, Cimicifuga, Cinnamon fern, Creeping Jenny, Ferns (Many), Convallaria, Corylus, Cotton grass, Cornus, Cotula, Cyclamen, Danae, Dicentra, Epimedium, Euonymus, Filipendula, Fritillaria, Galium, Gentiana, Helleborus, Hemerocallis, Hemp agrimony, Hepatica, Heucherella, Hosta, Honeysuckle, Hydrangea, Ligularia, Liriope, Lisichiton, Lilium, Lonicera, Lupinus, Lychnis, Lythrum, Meconopsis, Mimulus, Miscanthus, Peltiphylum (Darmera) Phyllostachys, Polygonum, Primula, Ranunculus, Rhamnus, Rheum, Rhododendron, Rodgersia, Royal Fern, Rubus, Sasa veitchii, Saxifraga, Senecio, Sinarundinaria, Sium suave, Skullcap, Tellima, Viola, Weigela