Drains!
Depending on the area and the slope involved. Is this a long-standing problem - is it only an issue after heavy rain or all year round?
Could you make use of the damper area to grow plants that like the damp that don't do well in drier parts of the garden?

Can you channel the water in a different direction?

Iris would be happy there and be no trouble at all.

How big of an area is it? If you do provide a method for drainage where is the water going to drain to, onto the street or onto a neighbors property? Don't try to wing this yourself. Get a professional that deals with this kind of problem.

Depends what iris though Diane. But it would be easier to turn the area into a bed of things that like wet ground, and make a feature of it. (Sorry, just seen Urbanite suggested that too)

I have some Wild Iris that I scrounged from the edge of a fishing lake. They need water !

Urbanite and Steragram, I think that placing plants that like wet feet is an excellent idea and a great alternative. I would suggest yellow loosestrife, purple loosestrife (the legal one), cardinal flower, beebalm, and hosta varieties to name a few.