to ATP, Searie. Hm, sort of depends upon how much sun it gets and how warm your climate is as well. What part of the country/world are you gardening in? (you could add this to your profile and then it will appear in all your posts)
If it's warm enough in the summer, a lot of perennial gingers really like lots of water, and can take some shade. If there is sun, Cannas would be my choice, for fabulous flowers that keep right on blooming until the weather gets too cold. You would need to mulch them heavily for the winter, though.
Why does that bed stay so wet? Is there drainage off the roof that lands in there? That would mean probably lifting perennials for the winter and potting them up. Wet feet in cold weather is a whole lot more destructive than in warm weather.