Answer: A number of perennials will do well in an area that is relatively damp or moist, but few will do well in actual standing water. Some that like moist conditions would include Siberian and Japanese iris, daylilies (hemerocallis), Joe Pye Weed, bee balm, hosta, astilbe, lobelia cardinalis and canna.
Unfortunately, I can't think of a vegetable to suggest. Vegetables as a rule prefer a situation in full sun with soil that is evenly moist but also well drained (not soggy) so you might want to consider making some raised beds.
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