Wetlands Planting Ideas

[Sam]

My backyard has very poor drainage due to a fair amount of clay and high
water table, not to mention a spring.
Over the years I have tried various remedies including, among other things,
drainage pipe to carry the water away.
Still the water persists with weeds and wild grass that can't be mowed due
to the muddy conditions.
I should also mention that the area is mostly shady with several trees.
So...I have given up trying to fight the water and I am resigned to work
with it, not fight it.
I would appreciate ideas/suggestions given these conditions.
Perhaps certain low-maintenance plants, wildflowers, bushes can co-exist
with the grass and thrive in the wet environment.
A weeping willow sucks up water but that brings its own maintenance issues.
I've also considered just dumping stone but prefer a natural environment
with plantings. Thanks for any ideas!
Sam

[Accepted1]

A fish pond with water pump for waterfall would look great. Where do you
live? That would determine the plants you would want to use.