Creeping Jenny is great, although the flowers aren't too thrilling. I like the yellowish green variety. Chameleon plant is great if you don't mind REALLY invasive.

I'll definitely second watergal on the creeping jenny -- and it is such a lovely plant, who cares if it ever flowers.

But the chameleon (houttuynia) is invasive even under dry conditions (I love invasives in general, and have some houttuynia in my rock garden) ~~ if kept moist, it turns into The Monster that Ate The Garden. After it finishes covering the flowerbed, it'll eat the lawn, too.

Rather than a groundcover, how about one of the dwarf grasses -- there's a carex that loves it wet

Pat

Mazus reptans has worked well for me in these conditions. It flowers purple or white ('alba') mostly in the spring, with some intermittent summer flowers. I actually have this mixed in with the yellow ('aurea') creeping jenny that watergal mentions above, so there is bright color even when there are no flowers. I think that Vinca minor, which also flowers in spring, would also do okay in your conditions. Both the creeping jenny and the vinca minor spread quickly, but are fairly easy to keep in check in my yard by pulling here and there. In a completely different vein (annual), I wonder if New Guinea impatiens -- i.e., the kind that like sun -- would mind wet feet; might be something to explore, if flowers rather than foliage is the main concern. Good luck.

Might try ceratostigma plumbaginoides. Fall flowering with red foliage color. I love it and it will do well in wet sunny sites.